Question

1) In a sample of 51 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population standard deviation is 2.7 degrees. What would be the 88% confidence interval for the temperatures in the freezer?

2) Determine the minimum sample size required when you want to be 85% confident that the sample mean is within two units of the population mean. Assume a population standard deviation of 4.3 in a normally distributed population.

Answer 1

1. As population standard deviation is known we will use z distribution to find CI

z value for 88% CI is 1.555 as P(-1.555<z<1.555)=0.88

So Margin of Error is

So CI is

2. Here z value for 85% CI is 1.44 as P(-1.44<z<1.44)=0.85

Margin of Error is E=2

So we will find n using formula of E