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. What is the probability that the person is between 65 and 69 inches?

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Iris 4 weeks 2021-09-17T14:30:12+00:00 1 Answer 0

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    2021-09-17T14:31:36+00:00

    Answer: the probability that the person is between 65 and 69 inches is 0.54

    Step-by-step explanation:

    Since the height for Asian adult males is normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x – µ)/σ

    Where

    x = height for Asian adult males.

    µ = mean height

    σ = standard deviation

    From the information given,

    µ = 66 inches

    σ = 2.5 inches

    We want to find the probability that the person is between 65 and 69 inches. It is expressed as

    P(65 ≤ x ≤ 69)

    For x = 65

    z = (65 – 66)/2.5 = – 0.4

    Looking at the normal distribution table, the probability corresponding to the z score is 0.34

    For x = 69

    z = (69 – 66)/2.5 = 1.2

    Looking at the normal distribution table, the probability corresponding to the z score is 0.88

    Therefore,

    P(65 ≤ x ≤ 69) = 0.88 – 0.34 = 0.54

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