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

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