What shape do you think the distribution of all possible sample means of 40 will have? Discuss.

SeaFair Fashions relies on its sales force of 220 to do an initial screening of all new fashion. The company is currently bringing out a new line of swimwear and has invited 40 salespeople to its Orlando home office. An issue of constant concern to the SeaFair sales office is the volume of orders generated by each salesperson. Last year, the overall company average was $417,330 with a standard deviation of $45,285. (Hint: The finite population correction factor, Equation 7.5, is required.)
⦁ Determine the probability the sample of 40 will have a sales average less than $400,000.
⦁ What shape do you think the distribution of all possible sample means of 40 will have? Discuss.

⦁ Determine the scale of the standard deviation of the distribution of the sample mean of all possible samples of size 40.
⦁ How would the answers to parts a, b and c change if the home office brought 60 salespeople to Orlando? Provide the respective answers for this sample size.
⦁ Each year SeaFair invites the sales personnel with sales above the 85th percentile to enjoy a complementary vacation in Hawaii. Determine the smallest average salary for the sales personnel that were in Hawaii last year. (Assume the distribution of sales was normally distributed last year.)


United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems. United supplies these valves to major companies such as Rain Bird and Nelson, who in turn sell sprinkler products to retailers. United recently entered into a contract to supply 40,000 sprinkler valves. The contract called for at least 97% of the valves to be free of defects. Before shipping the valves, United managers tested 200 randomly selected valves and found 190 defect-free valves in the sample. The managers wish to know the probability of finding 190 or fewer defect-free valves if in fact the population of 40,000 valves is 97% defect-free. Discuss how they could use this information to determine whether to ship the valves to the customer.


Allante Pizza delivers pizzas throughout its local market area at no charge to the customer. However, customers often tip the driver. The owner is interested in estimating the mean tip income per delivery. To do this, she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers. These data are

$2.25 $2.50 $2.25 $2.00 $2.00 $1.50
$0.00 $2.00 $1.50 $2.00 $3.00 $1.50

⦁ Based on these sample data, what is the best point estimate to use as an estimate to use as an estimate of the true mean tip per delivery?

⦁ Suppose the owner is interested in developing a 90% confidence interval estimate. Given the fact that the population standard deviation is unknown, what distribution will be used to obtain the critical value?

⦁ Referring to part b, what assumption is required to use the specifies distribution to obtain the critical value? Develop a box and whisker plot to illustrate whether this assumption seems to be reasonably satisfied.

⦁ Referring to parts b and c, construct and interpret the 90% confidence interval estimate for the population mean.


The Northwest Pacific Phone Company wishes to estimate the average number of minutes its customers spend on long-distance calls per month. The company wants the estimate made with 99% confidence and a margin of error of no more than 5 minutes.

⦁ A previous study indicated that the standard deviation for long-distance calls is 21 minutes per month. What should the sample size be?

⦁ Determine the required sample size if the confidence level were changed from 99% to 90%.

⦁ What would the required sample size be if the confidence level was 95% and the margin of error was 8 minutes?


As the automobile accident rate increases, insurers are forced to increase their premium rates. Companies such as Allstate have recently been running a campaign they hope will result in fewer accidents by their policyholders. For each six-month period that a customer goes without an accident, Allstate will reduce the customer’s premium rate by a certain percentage. Companies like Allstate have reason to be concerned about driving habits, based on a survey conducted by Drive for Life, a safety group sponsored by Volvo of North America, in which 1,100 drivers were surveyed. Among those surveyed, 74% said that careless or aggressive driving was the biggest threat on the road. One-third of the respondents said that cell phone usage by other drivers was the driving behavior that annoyed them the most. Based on these data, assuming that the sample was a simple random sample, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users.

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