A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability t

Question

A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 100 and X = 130?​

in progress 0
Aaliyah 2 weeks 2021-09-28T17:51:35+00:00 1 Answer 0

Answers ( )

    0
    2021-09-28T17:52:56+00:00

    Answer: P(100 ≤ x ≤ 130) = 0.43

    Step-by-step explanation:

    Since the scores are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x – µ)/σ

    Where

    x = scores

    µ = mean score

    σ = standard deviation

    From the information given,

    µ = 100

    σ = 20

    We want to find the probability that the scores is between 100 and 130. It is expressed as

    P(100 ≤ x ≤ 130)

    For x = 100,

    z = (100 – 100)/20 = 0

    Looking at the normal distribution table, the probability corresponding to the z score is 0.5

    For x = 100,

    z = (130 – 100)/20 = 1.5

    Looking at the normal distribution table, the probability corresponding to the z score is 0.93

    Therefore,

    P(100 ≤ x ≤ 130) = 0.93 – 0.5 = 0.43

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )