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.

Question

Chaz Stanton

SAT

11 October, 01:03

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.

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Dominique Reed · 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%