Question

A population of values has a normal distribution with μ=25.9 and σ=74.2. You intend to draw a random sample of size n=99.Find the probability that a sample of size n=99 is randomly selected with a mean between 28.1 and 35.6. P(28.1 < M < 35.6) =

Answer 1

Answer: 0.0397

Step-by-step explanation

Given

• Normal distribution

,

• μ = 25.9

• σ = 74.2

,

• n = 99

,

• Mean between 28.1 and 35.6

Procedure

As we have a normal distribution, we can get Z-score to approximate the probability using the following formula for both values:

`Z=(x-\mu)/(\sigma)`

• Lower value

`Z_1=(28.1-25.9)/(74.2)=0.030`

• Upper value

`Z_2=(35.6-25.9)/(74.2)=0.131`