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12. A bank wanted to use a sample of account balances to estimate the mean savings...

12.
A bank wanted to use a sample of account balances to estimate the mean savings of its customers.
a) A small pilot study found the savings to be approximately normally distributed with a mean of $1410 and a standard deviation of $242. A 99% confidence interval is to be used and a maximum error of $42 is desired. How many customers should be sampled?
[3]
b) In the sample, 114 people had savings greater than $1000. Using the sample size you found in a), find the 90% confidence interval for the population proportion. Interpret your results.

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