Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,0

Question

Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value will be between $62,500 and $64,000

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Liliana 2 weeks 2022-01-06T22:47:35+00:00 1 Answer 0 views 0

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    2022-01-06T22:49:17+00:00

    Answer:

    0.2009

    Step-by-step explanation:

    Mean(μ) = 65000

    Standard deviation (σ) = 7000

    n = 25

    Let X be the random variable which is a measure of salaries of university professors

    Z = (μ – x) /σ/√n

    Pr(62500 ≤ x ≤ 64000) = ???

    Pr((65000 – 62500)/7000/√25 ≤ z ≤ (65000 – 64000) / 7000/√25)

    = Pr(2500 / 7000/5 ≤ z ≤ 1000 / 7000/5)

    = Pr(2500 / 1400 ≤ z ≤ 1000/1400)

    = Pr(1.79 ≤ z ≤ 0.714)

    = Pr(0 ≤ z ≤ 1.79) – Pr(0 ≤ z ≤ 0.714)

    From the normal distribution table we have

    0.4633 – 0.2624

    = 0.2009

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