1) In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.8 days. How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 1 day?

2) A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 98% confident that the true mean is within 3 ounces of the sample mean? The standard deviation of the birth weights is known to be 6 ounces.

3) A recent survey found that 71% of all adults over 50 wear glasses for driving. You randomly select 30 adults over 50, and ask if he or she wears glasses. Decide whether you can use the normal distribution to approximate the binomial distribution. If so, find the mean and standard deviation, If not, explain why.

4) After Hurricane Sandy, homeowners in one town that was not directly struck filed insurance claims that averaged $23,500 with a standard deviation of $500. If 64 claims are examined, what proportion of those will be more than $23,650?