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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 :

Answer: 0.0397

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:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

• Lower value

[tex]Z_1=\frac{28.1-25.9}{74.2}=0.030[/tex]

• Upper value

[tex]Z_2=\frac{35.6-25.9}{74.2}=0.131[/tex][tex]P\left(28.1Using the Standard Normal Table we can conclude that:[tex]P(28.1\lt M\lt35.6)=P(0.030\lt Z\lt0.131)=0.0397[/tex]

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