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

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 .