The mean per capita consumption of milk per year is 152 liters with a variance of 484. If a sample of 109 people is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 3.27 liters

0.93965

Step-by-step explanation:

The z score when given a random number of samples =

z = (x-μ)/σ/√n, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

n is the random number of samples

x-μ = 3.27

Standard deviation = √Variance

= √484 = 22

n = 109

z = 3.27/22/√109

z = 3.27/2.1072178275

z = 1.55181

Probability value from Z-Table:

P(x< 155.27) = 0.93965

The probability that the sample mean would differ from the true mean by less than 3.27 liters is 0.93965