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The mean per capita consumption of milk per year is 140 liters with a standard deviation of 22 liters. If a sample of 233 people is randomly selected, what is the probability that the sample mean would be less than 137.01 liters? Round your answer to four decimal places.

User DanielKhan
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1 Answer

4 votes

Answer: 0.0192

Explanation:

Given : The mean per capita consumption of milk per year :
\mu=140\text{ liters}

Standard deviation :
\sigma=22\text{ liters}

Sample size :
n=233

Let
\overline{x} be the sample mean.

The formula for z-score in a normal distribution :


z=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}

For
\overline{x}=137.01


z=(137.01-140)/((22)/(√(233)))\approx-2.07

The P-value =
P(\overline{x}<137.01)=P(z<-2.07)= 0.0192262\approx 0.0192

Hence, the probability that the sample mean would be less than 137.01 liters is 0.0192 .

User Bulkin
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