# Expert Answers

1. Assume that the number of sales per day of an app in the Apple IOS App store is normally distributed.

A) What two parameters of the distribution would you need to be able to determine the probability of sales on a particular day exceeding 100 units?

B) If the probability of sales exceeding 100 units is 20% and the mean daily sales is 86 units, then what is the standard deviation of distribution?

2. Researchers are studying a new chemical process for producing dyes. Although they don't know it, the yield of the process is normally distributed with u=550kg and O=75kg. The researchers plan to estimate the products mean yield by running the process 35 times, recording the yield each time. Have they chosen a large enough sample to be 90% confident that their computed mean will be within 20kg of the actual mean? Show your work to justify your answer

3. A health inspector at a restaurant will enter the kitchen and choose 5 stations to inspect from a predetermined list of 15 stations present in most restaurant kitchens.

a. How many different sets of 5 stations exist?

b. If all sets are equally likely, what is the probability of each set?

c. If the inspector were instead to randomly select 13 stations to inspect, how many different sets of 13 stations would exist?

d. If all sets were equally likely, what is the probability of each set?

4. The company policy for customer service representatives gives time off for positive reviews. If, in the first 20 calls a customer service agent handles In a day, 13 or more elect to take a subsequent survey and rate the service as "excellent," then the company gives the agent his or her final hour of work that day off, paid. Ellie receives excellent reviews from about 30% of the calls she handles. Assuming she always receives at least 20 calls in the first 7 hours of a workday, on what percentage of her 8-hour workdays does Ellie get the final hour off?

5. A quality control analyst measures the number of hours a patient in a low-risk condition waits for care at the emergency room of a small hospital. The following data are obtained for 20 patients.

2.26, 2.01, 3.0, 1.22, 1.92, 1.79, 0.78, 1.89, 0.71, 1.58

2.02, 2.77, 2.87, 0.51, 0.74, 1.95, 2.76, 2.61, 3.54, 2.95

a) Compute the sample mean, sample median, and range of the data

b) Compute the sample standard deviation and sample variation.

6. Since careful records have begun being kept in January, Ericâ€™s small business has delivered the following quantities of flowers throughout town.

January February March April May June July August

Small Bouquets 85 34 26 24 43 29 30 19

Large Bouquets 23 64 27 18 33 23 20 13

Assuming the data is normally distributed construct two separate 90% confidence intervals one for the number of deliveries of small bouquets in September and one for the number of large bouquets in September.

9. Consider the following data values of a variable x and y

X 5, 4 3 6 9 8 10

y 7 8 10 5 2 3 1

Construct a scatter diagram for the data points and plot the least squares regression line on it. Find the least squares regression line.

7. A quality control experiment is to be done on a machine that fills tubes with toothpaste. Its specifications require that it fill tubes with 4.7 oz. A random sample of 40 tubes filled by the machine is taken and each tube is weighed. The resulting data are below, with the weighed. The data are below, with the tube already having been subtracted from each. Perform a hypothesis test at the 90% confidence level to determine if the machine is performing according to specification.

4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56

4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75

4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74

4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69

A) What two parameters of the distribution would you need to be able to determine the probability of sales on a particular day exceeding 100 units?

B) If the probability of sales exceeding 100 units is 20% and the mean daily sales is 86 units, then what is the standard deviation of distribution?

2. Researchers are studying a new chemical process for producing dyes. Although they don't know it, the yield of the process is normally distributed with u=550kg and O=75kg. The researchers plan to estimate the products mean yield by running the process 35 times, recording the yield each time. Have they chosen a large enough sample to be 90% confident that their computed mean will be within 20kg of the actual mean? Show your work to justify your answer

3. A health inspector at a restaurant will enter the kitchen and choose 5 stations to inspect from a predetermined list of 15 stations present in most restaurant kitchens.

a. How many different sets of 5 stations exist?

b. If all sets are equally likely, what is the probability of each set?

c. If the inspector were instead to randomly select 13 stations to inspect, how many different sets of 13 stations would exist?

d. If all sets were equally likely, what is the probability of each set?

4. The company policy for customer service representatives gives time off for positive reviews. If, in the first 20 calls a customer service agent handles In a day, 13 or more elect to take a subsequent survey and rate the service as "excellent," then the company gives the agent his or her final hour of work that day off, paid. Ellie receives excellent reviews from about 30% of the calls she handles. Assuming she always receives at least 20 calls in the first 7 hours of a workday, on what percentage of her 8-hour workdays does Ellie get the final hour off?

5. A quality control analyst measures the number of hours a patient in a low-risk condition waits for care at the emergency room of a small hospital. The following data are obtained for 20 patients.

2.26, 2.01, 3.0, 1.22, 1.92, 1.79, 0.78, 1.89, 0.71, 1.58

2.02, 2.77, 2.87, 0.51, 0.74, 1.95, 2.76, 2.61, 3.54, 2.95

a) Compute the sample mean, sample median, and range of the data

b) Compute the sample standard deviation and sample variation.

6. Since careful records have begun being kept in January, Ericâ€™s small business has delivered the following quantities of flowers throughout town.

January February March April May June July August

Small Bouquets 85 34 26 24 43 29 30 19

Large Bouquets 23 64 27 18 33 23 20 13

Assuming the data is normally distributed construct two separate 90% confidence intervals one for the number of deliveries of small bouquets in September and one for the number of large bouquets in September.

9. Consider the following data values of a variable x and y

X 5, 4 3 6 9 8 10

y 7 8 10 5 2 3 1

Construct a scatter diagram for the data points and plot the least squares regression line on it. Find the least squares regression line.

7. A quality control experiment is to be done on a machine that fills tubes with toothpaste. Its specifications require that it fill tubes with 4.7 oz. A random sample of 40 tubes filled by the machine is taken and each tube is weighed. The resulting data are below, with the weighed. The data are below, with the tube already having been subtracted from each. Perform a hypothesis test at the 90% confidence level to determine if the machine is performing according to specification.

4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56

4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75

4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74

4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69

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