Question

the number of motorcycles sold annually by salespeople is normally distributed with a standard deviation of 15. A random sample of 300 salesperson taken and the mean number of motorcycles sold annually was found to be 75. find the 99% confidence interval estimate of the population mean

Answer 1

$99\%CI=(\bar x-z_{0.005}\frac{\sigma}{\sqrt{n}},\bar x+z_{0.005}\frac{\sigma}{\sqrt{n}})=$

$=(75-2.58\frac{15}{\sqrt{300}}, 75+2.58\frac{15}{\sqrt{300}})=(74.66, 75.34).$