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The height of 5th grade boys is normally distributed with mean μ=57 inches and standard deviation σ=2 inches. What is the probability that the height of a randomly selected 5th grade boy will be between 53 inches and 61 inches?

1 Answer

6 votes

Answer:

0.9544

Explanation:

Mean = μ=57

Standard deviation σ=2

Formula :
z=(x-\mu)/(\sigma)

At x = 53


z=(53-57)/(2)


z=-2

Refer the z table

P(z<-2)=0.0228

At x = 61


z=(61-57)/(2)


z=2

Refer the z table

P(z<2)=0.9772

We are suppose to find the probability that the height of a randomly selected 5th grade boy will be between 53 inches and 61 inches.

P(53<x<61)=P(-2<z<2)=P(z<2)-P(z<-2) = 0.9772 - 0.0228=0.9544

Hence the probability that the height of a randomly selected 5th grade boy will be between 53 inches and 61 inches is 0.9544

User Per Melin
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