# Find the mean for the given sample data

1. Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score. 536,608,344,340,596,357,343,566,470,482

464.2

476.0

473.7

455.1

2. Find the midrange for the given sample data. Listed below are the amounts of time (in months) that the employees of an electronics company have been working at the company. Find the midrange. 12,21,26,37,46,53,61,66,75,76,85,91,132,155

63.5 months

71.5 months

66.9 months

83.5 months

3. Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 20.0,21.5,27.4,47.3,13.1,11.1

4145.12

37.34

13.11

3285.46

4. Find the indicated probability. A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).

1/3

3/2

6

2/3

5. Find the indicated probability. Round to the nearest thousandth. In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive?

0.00000177

1.000

0.503

0.497

6. Evaluate the expression. 11C4

330

1980

5040

3

7. Provide an appropriate response. Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?

-$3.00

$3.00

-$1.33

$5.00

8. Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Find the probability of selecting 2 or more girls.

0.999

0.006

0.001

0.994

9. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen.

Not binomial: there are more than two outcomes for each trial.

Procedure results in a binomial distribution.

Not binomial: the trials are not independent.

Not binomial: there are too many trials.

10. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 4, x = 3, p = 1/6

0.015

0.023

0.012

0.004

11. Use the Poisson model to approximate the probability. Round your answer to four decimal places. The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 140 calls received by the switchboard, there are no wrong numbers.

0.0608

0.1703

0.9392

0.8297

0.0669

12. Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.843, n = 5

Critical values: r = ±0.878, significant linear correlation

Critical values: r = ±0.950, no significant linear correlation

Critical values: r = 0.950, significant linear correlation

Critical values: r = ±0.878, no significant linear correlation

13. Find the value of the linear correlation coefficient r. The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test.

0.224

-0.678

0.678

-0.224

14. If z is a standard normal variable, find the probability. The probability that z is greater than -1.82

0.4656

0.9656

-0.0344

0.0344

15. Solve the problem. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.

0.0287

0.1179

0.4713

0.3821

16. The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of no more than 75 defective CD's

The area to the right of 75.5

The area to the left of 75

The area to the left of 74.5

The area to the left of 75.5

17. Use the normal distribution to approximate the desired probability. Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives.

0.1871

0.4936

0.2946

0.3229

18. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. In a random sample of 184 college students, 97 had part-time jobs. Find the margin of error for the 95% confidence interval used to estimate the population proportion.

0.0721

0.00266

0.126

0.0649

19. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 125, x = 72; 90% confidence

0.507 < p < 0.645

0.503 < p < 0.649

0.506 < p < 0.646

0.502 < p < 0.650

20. Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.015; confidence level: 96%; unknown

6669

3667

4519

4670

21. Solve the problem. Round the point estimate to the nearest thousandth. 50 people are selected randomly from a certain population and it is found that 13 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall?

0.50

0.26

0.19

0.74

22. Use the confidence level and sample data to find a confidence interval for estimating the population (mu). Round your answer to the same number of decimal places as the sample mean. A random sample of 130 full-grown lobsters had a mean weight of 21 ounces and a standard deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean mu.

21 oz < mu < 23 oz

20 oz < mu < 22 oz

20 oz < mu < 23 oz

19 oz < mu < 21 oz

23. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. = 0.05 for a left-tailed test.

-1.96

±1.96

±1.645

-1.645

24. Find the value of the test statistic z using z = The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls.

3.96

-3.96

4.71

-4.71

25. use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a right-tailed test is z = 1.43.

0.1528; fail to reject the null hypothesis

0.1528; reject the null hypothesis

0.0764; fail to reject the null hypothesis

0.0764; reject the null hypothesis

464.2

476.0

473.7

455.1

2. Find the midrange for the given sample data. Listed below are the amounts of time (in months) that the employees of an electronics company have been working at the company. Find the midrange. 12,21,26,37,46,53,61,66,75,76,85,91,132,155

63.5 months

71.5 months

66.9 months

83.5 months

3. Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 20.0,21.5,27.4,47.3,13.1,11.1

4145.12

37.34

13.11

3285.46

4. Find the indicated probability. A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).

1/3

3/2

6

2/3

5. Find the indicated probability. Round to the nearest thousandth. In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive?

0.00000177

1.000

0.503

0.497

6. Evaluate the expression. 11C4

330

1980

5040

3

7. Provide an appropriate response. Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?

-$3.00

$3.00

-$1.33

$5.00

8. Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Find the probability of selecting 2 or more girls.

0.999

0.006

0.001

0.994

9. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen.

Not binomial: there are more than two outcomes for each trial.

Procedure results in a binomial distribution.

Not binomial: the trials are not independent.

Not binomial: there are too many trials.

10. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 4, x = 3, p = 1/6

0.015

0.023

0.012

0.004

11. Use the Poisson model to approximate the probability. Round your answer to four decimal places. The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 140 calls received by the switchboard, there are no wrong numbers.

0.0608

0.1703

0.9392

0.8297

0.0669

12. Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.843, n = 5

Critical values: r = ±0.878, significant linear correlation

Critical values: r = ±0.950, no significant linear correlation

Critical values: r = 0.950, significant linear correlation

Critical values: r = ±0.878, no significant linear correlation

13. Find the value of the linear correlation coefficient r. The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test.

0.224

-0.678

0.678

-0.224

14. If z is a standard normal variable, find the probability. The probability that z is greater than -1.82

0.4656

0.9656

-0.0344

0.0344

15. Solve the problem. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.

0.0287

0.1179

0.4713

0.3821

16. The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of no more than 75 defective CD's

The area to the right of 75.5

The area to the left of 75

The area to the left of 74.5

The area to the left of 75.5

17. Use the normal distribution to approximate the desired probability. Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives.

0.1871

0.4936

0.2946

0.3229

18. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. In a random sample of 184 college students, 97 had part-time jobs. Find the margin of error for the 95% confidence interval used to estimate the population proportion.

0.0721

0.00266

0.126

0.0649

19. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 125, x = 72; 90% confidence

0.507 < p < 0.645

0.503 < p < 0.649

0.506 < p < 0.646

0.502 < p < 0.650

20. Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.015; confidence level: 96%; unknown

6669

3667

4519

4670

21. Solve the problem. Round the point estimate to the nearest thousandth. 50 people are selected randomly from a certain population and it is found that 13 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall?

0.50

0.26

0.19

0.74

22. Use the confidence level and sample data to find a confidence interval for estimating the population (mu). Round your answer to the same number of decimal places as the sample mean. A random sample of 130 full-grown lobsters had a mean weight of 21 ounces and a standard deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean mu.

21 oz < mu < 23 oz

20 oz < mu < 22 oz

20 oz < mu < 23 oz

19 oz < mu < 21 oz

23. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. = 0.05 for a left-tailed test.

-1.96

±1.96

±1.645

-1.645

24. Find the value of the test statistic z using z = The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls.

3.96

-3.96

4.71

-4.71

25. use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a right-tailed test is z = 1.43.

0.1528; fail to reject the null hypothesis

0.1528; reject the null hypothesis

0.0764; fail to reject the null hypothesis

0.0764; reject the null hypothesis

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