A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 52 meet the specification for puncture resistance.
a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification.
b. Find a 90% confidence interval for the proportion of cans in the shipment that meet the specification.
c. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05.
d. Find the sample size needed for a 90% confidence interval to specify the proportion to within ±0.05.
e. If a 90% confidence interval is computed each day for 300 days, what is the probability that more than 280 of the confidence intervals cover the true proportions?