1. A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 80 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 80 cans, 66 meet the specification for puncture resistance. a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification. Round the answers to three decimal places. b. Find a 90% confidence interval for the proportion of cans in the shipment that meet the specification. Round the answers to three decimal places. c. 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? Round the answer to three decimal places.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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1. A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 80
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 80 cans, 66 meet the specification for puncture
resistance.
a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification.
Round the answers to three decimal places.
b. Find a 90% confidence interval for the proportion of cans in the shipment that meet the specification.
Round the answers to three decimal places.
c. 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? Round the answer to three decimal places.
Transcribed Image Text:1. A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 80 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 80 cans, 66 meet the specification for puncture resistance. a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification. Round the answers to three decimal places. b. Find a 90% confidence interval for the proportion of cans in the shipment that meet the specification. Round the answers to three decimal places. c. 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? Round the answer to three decimal places.
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