Consider a sample of nine wait times measured in seconds

1. Consider a sample of nine wait times measured in seconds at a drive through coffee shop. The sample mean is 95 and the sample standard deviation is 23.516. The population mean and standard deviation are 100 and 20 respectively. (1) What is the size of the sampling error in this case?

a. (What is the probability that the average wait time would be less than 80 seconds?

b. (What is the probability that the average wait time would be more than 109 seconds?

c. (What is the probability that the average wait time would be between 90 and 95 seconds?

d. What is the probability that a customer waits more than 65 seconds?

2. A company receives 20 faxed orders every two hours

a. What is the probability that it will receive 8 orders in the next hour?

b. What is the probability that an order will be faxed within the next 9 minutes?

c. What is the probability that more than 12 minutes will elapse between faxed orders?

d. The company also receive online orders. These orders are over $200 on average 15% of the time. What is the probability that in a sample of 10 online orders, 5 or 6 will be over $200?

 

3. The student body of a local college draws 40% of its students from Ontario, 35% from the rest of Canada, and the remainder from outside Canada. Of those from Ontario, 60% are female, of those from the rest of Canada 25% are female, and of those from outside Canada, 15% are female.

a. What is the probability of a male student from Ontario?

b. What is the probability of a male student who did not come from Ontario?

 

4. (A company is reviewing the performance of two different suppliers of toner ink as their intention is to compare them and possibly switch to the alternate one. Using the following data for hours of toner use before empty answer the following.

	CURRENT SUPPLIER A	ALTERNATE SUPPLIER B
Mean	501.7	495.3
Variance	102.3	20.1
Observations	20	20

df = n1+n2-2 = 38 AND

a. Determine if the standard deviation of the Alternate Supplier B is significantly less than 5. Use alpha = 0.05.

b. Assuming that the variances of the two are not equal, test to determine if the Current Supplier A has more than 2 hours average hours of toner use than Alternate Supplier B. Use alpha = 0.05.

c. What is your recommendation to the company with respect to the supplier to select? Explain.

 

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