1. Suppose that a random sample of 40 power window mechanisms is taken from a lot supplied to

an auto manufacturer. Each sampled mechanisms are tested by putting it through continuous

up-down cycles until it fails. Suppose that in the entire lot, the mean time to failure is 4200

cycles and that the standard deviation 3400. The mean failure time for the sample is recorded.

a. Would it be reasonable to assume that the distribution of individual failure times

should be roughly normal?

b. Would it be reasonable to assume that the distribution of sample mean should be

roughly normal?

2. the number of minutes that diners spend at the table has a major impact on the profitability of

the restaurant. Suppose the average number of minutes that diners spend at a table for dinner at

the restaurant is 90 minutes with a standard deviation of 15 minutes.

a. Calculate the probability that a diner spends at his/her table for dinner will be less than 100

minutes.

b. Calculate the probability that the average number of minutes that diners spend at their table

for the sample of 45 diners will be less than100 minutes.

c. Calculate the probability that the average number of minutes that diners spend at their table

for the sample of 45 diners will be less than 80 minutes.

3. A restaurant tried to increase business on Monday night, by featuring a special $1.00 dessert

menu. The number of diners on each of 11 Mondays recorded while the special menu was in

effect. The data were

119 139 112 126 128 108 63 118 105 131 142

a. Find a 95% confidence interval the long-run number of diners.

b. Before the special menu, the restaurant average 105.2 diners per Monday night. Is it

reasonable to interpret the confidence interval from part “a” as indicating that the special menu

did not increase the average number of diners?

Suppose that a random sample of 40 power window mechanisms is taken from a lot supplied to an auto manufacturer. Each sampled mechanisms are tested by putting it through continuous up-down cycles until it fails. Suppose that in the entire lot, the mean time to failure is 4200 cycles and that the standard deviation 3400. The mean failure time for the sample is recorded. a. Would it be reasonable to assume that the distribution of individual failure times should be roughly normal? b. Would it be reasonable to assume that the distribution of sample mean should be