Question

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.

Answer 1

Answer: 0.0192

Step-by-step 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 :

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For  $\overline{x}=137.01$

$z=\dfrac{137.01-140}{\dfrac{22}{\sqrt{233}}}\approx-2.07$

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 .