# Numerical variables - Answers

Question 1 of 25

Numerical variables can be subdivided into which two types?

A.Diverse and categorical

B.Cross-sectional and discrete

C.Discrete and continuous

D.Nominal and progressive

Question 2 of 25

If a menu has a choice of 4 appetizers, 4 main courses, and 3 desserts, then the sample space for all possible dinners has how many outcomes?

A.48

B.16

C.28

D.3

Question 3 of 25

If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is

A.1.20

B.0.80

C.0.32

D.0.40

Question 4 of 25

A pet supplier has a stock of parakeets of which 10% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

A.0.081

B.0.243

C.0.027

D.0.003

Question 5 of 25

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.

x 0 1 2 3 4 5

P (X=x) 0.20 0.25 0.20 0.15 0.10 0.10

What is the variance of X?

A.2.50

B.2.34

C.4.32

D.3.42

Question 6 of 25

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that greater than 30 batteries will last at least 8 hours?

A.0.0848

B.0.8594

C.0.9152

D.0.9522

Question 7 of 25

The standard normal distribution has a mean of ___ and standard deviation of ___, respectively.

A.1 and 1

B.1 and 0

C.0 and 1

D.0 and 0

Question 8 of 25

If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

A.one standard deviation higher than the mean

B.to the right of the mean

C.to the left of the mean

D.equal to the mean

Question 9 of 25

The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:

A.point estimate theorem

B.central limit theorem

C.simple random sample theorem

D.central tendency theorem

Question 10 of 25

Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 < X < 90) is

A.0.5328

B.0.1498

C.0.3413

D.0.1915

Question 11 of 25

In a normal distribution, changing the standard deviation:

A.makes the curve more or less spread out

B.splits the distribution to two curves

C.shifts the curve left or right

D.makes the curve more robust

Question 12 of 25

Find the probability, P(Z < 0.17), using the standard normal distribution.

A..8300

B..4325

C..5675

D..0675

Part 5 of 9 -

Question 13 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The following data are the base salaries, in thousands of dollars, of 50 chief executive officers for a sample of companies doing business with the state of Connecticut. That is, the first entry in the table below corresponds to a salary of $125,000. A copy of this data set can be found in the Excel Workbook called CEOSalaries.xls.

125 157 113 127 201

165 145 119 148 158

148 168 117 105 136

136 125 148 108 178

179 191 225 204 104

205 197 119 209 157

209 205 221 178 247

235 217 222 224 187

265 148 165 228 239

245 152 148 115 150

Find the interquartile range of the CEO salaries, in thousands of dollars, rounded to 2 decimal places. Do not use a dollar sign. Note: $177,760 should be recorded as 177.76.

CEOSalaries.xls

Part 6 of 9 -

Question 14 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer.

Question 15 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Find the mean of the following probability distribution?

1 0.20

2 0.10

3 0.35

4 0.05

5 0.30

Place your answer, rounded to two decimal places, in the blank. When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 1.23 would be a legitimate entry.

Part 7 of 9 -

Question 16 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was chocolate flavor, given that it was sold on a cone. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

Question 17 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

If a set of six books is to be placed on a shelf, in how many ways can the six books be arranged? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.

Part 8 of 9 -

Question 18 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.

Question 19 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.

How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry.

Question 20 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.

How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry.

Question 21 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.

Question 22 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What are the two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry.

Lower value

Upper value

Question 23 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

Find probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry.

Question 24 of 25

If Z is a standard normal variable, then P(Z = 1) = 0.3413.

True

False

Question 25 of 25

Using the standard normal curve, the probability or area between Z = -1.50 and Z = 1.50 is 0.4332.

True

False

Numerical variables can be subdivided into which two types?

A.Diverse and categorical

B.Cross-sectional and discrete

C.Discrete and continuous

D.Nominal and progressive

Question 2 of 25

If a menu has a choice of 4 appetizers, 4 main courses, and 3 desserts, then the sample space for all possible dinners has how many outcomes?

A.48

B.16

C.28

D.3

Question 3 of 25

If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is

A.1.20

B.0.80

C.0.32

D.0.40

Question 4 of 25

A pet supplier has a stock of parakeets of which 10% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

A.0.081

B.0.243

C.0.027

D.0.003

Question 5 of 25

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.

x 0 1 2 3 4 5

P (X=x) 0.20 0.25 0.20 0.15 0.10 0.10

What is the variance of X?

A.2.50

B.2.34

C.4.32

D.3.42

Question 6 of 25

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that greater than 30 batteries will last at least 8 hours?

A.0.0848

B.0.8594

C.0.9152

D.0.9522

Question 7 of 25

The standard normal distribution has a mean of ___ and standard deviation of ___, respectively.

A.1 and 1

B.1 and 0

C.0 and 1

D.0 and 0

Question 8 of 25

If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

A.one standard deviation higher than the mean

B.to the right of the mean

C.to the left of the mean

D.equal to the mean

Question 9 of 25

The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:

A.point estimate theorem

B.central limit theorem

C.simple random sample theorem

D.central tendency theorem

Question 10 of 25

Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 < X < 90) is

A.0.5328

B.0.1498

C.0.3413

D.0.1915

Question 11 of 25

In a normal distribution, changing the standard deviation:

A.makes the curve more or less spread out

B.splits the distribution to two curves

C.shifts the curve left or right

D.makes the curve more robust

Question 12 of 25

Find the probability, P(Z < 0.17), using the standard normal distribution.

A..8300

B..4325

C..5675

D..0675

Part 5 of 9 -

Question 13 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The following data are the base salaries, in thousands of dollars, of 50 chief executive officers for a sample of companies doing business with the state of Connecticut. That is, the first entry in the table below corresponds to a salary of $125,000. A copy of this data set can be found in the Excel Workbook called CEOSalaries.xls.

125 157 113 127 201

165 145 119 148 158

148 168 117 105 136

136 125 148 108 178

179 191 225 204 104

205 197 119 209 157

209 205 221 178 247

235 217 222 224 187

265 148 165 228 239

245 152 148 115 150

Find the interquartile range of the CEO salaries, in thousands of dollars, rounded to 2 decimal places. Do not use a dollar sign. Note: $177,760 should be recorded as 177.76.

CEOSalaries.xls

Part 6 of 9 -

Question 14 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer.

Question 15 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Find the mean of the following probability distribution?

1 0.20

2 0.10

3 0.35

4 0.05

5 0.30

Place your answer, rounded to two decimal places, in the blank. When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 1.23 would be a legitimate entry.

Part 7 of 9 -

Question 16 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was chocolate flavor, given that it was sold on a cone. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

Question 17 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

If a set of six books is to be placed on a shelf, in how many ways can the six books be arranged? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.

Part 8 of 9 -

Question 18 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.

Question 19 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.

How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry.

Question 20 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.

How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry.

Question 21 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.

Question 22 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What are the two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry.

Lower value

Upper value

Question 23 of 25

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

Find probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry.

Question 24 of 25

If Z is a standard normal variable, then P(Z = 1) = 0.3413.

True

False

Question 25 of 25

Using the standard normal curve, the probability or area between Z = -1.50 and Z = 1.50 is 0.4332.

True

False

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