Question

The mean per capita consumption of milk per year is 131 liters with a variance of 841. If a sample of 132 people is randomly selected, what is the probability that the sample mean would be less than 133.5 liters? Round your answer to four decimal places.

Answer 1

The probability that the the sample mean would be less than x=132.25 will be calculated as follows:
z=(x-σ)/μ
μ- mean
σ- standard deviation
z=(132.25-138)/28=-0.2054
thus:
P(X≤x)=0.4207=42.07%