According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a s

Question

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual. A) Give the distribution of X.

X ~ _____ (____,____)

B) Find the probability that the person is between 64 and 69 inches.

Write the probability statement.

P(______

What is the probability?

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Jade 2 weeks 2021-09-10T10:03:33+00:00 1 Answer 0

Answers ( )

    0
    2021-09-10T10:05:01+00:00

    Answer:   A) X\sim N(66,2.5)

    B)0.6731

    Step-by-step explanation:

    Given : The height for Asian adult males is normally distributed with

    Mean : \mu=66\text{ inches}

    Standard deviation : \sigma= 2.5\text{ inches}

    Let X = height of the individual.

    A) The distribution of X is given by :-

    X\sim N(\mu,\sigma)\\\\\Rightarrow\ X\sim N(66,2.5)

    B) The formula to find the z-score is given by  :-

    z=\dfrac{x-\mu}{\sigma}

    For , x= 64

    z=\dfrac{64-66}{2.5}=-0.8

    For , x= 69

    z=\dfrac{69-66}{2.5}=1.2

    Now, the required probability :-

    P(64<x<69)=P(-0.8<z<1.2)=P(z<1.2)-P(z<0.8)\\\\=0.8849303-0.2118554=0.6730749\approx0.6731

    Hence, the probability that the person is between 64 and 69 inches is 0.6731.

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