The cost of 5 gallons of ice cream has a variance of 49 with a mean of 30 dollars during the summer.

Question

What is the probability that the sample would differ from the true mean by less than 0.6 dollars if a sample of 145 5 gallon pails is randomly selected ? round to 4 decimals

Please explainn

Answer 1

Variance = 49; SD = √Variance = 7

Standard Error = SD/√N = 7/√145 ≈ 0.5813

Z = number of standard errors away from the mean = 0.6/SE = 0.6/0.5813 ≈ 1.0322

P(|Z| > 1.0322) = P(Z < -1.0322) + P(Z > +1.0322) ≈ 0.1534 + 0.1534 = 0.3068

There is a probability of 0.3068 (or 30.68%) that the sample mean price of a 5-gallon container of ice cream will differ from the population mean of 30 by 0.6 dollars.