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The Dean of a business school claims that the average weekly income of graduates of his...

The Dean of a business school claims that the average weekly income of graduates of his school one year after graduation is μ = $600 and σ =$100. If the Dean s claim is correct, what is the probability that n=25 randomly selected graduates have an average weekly income of less than $550 i.e. P(x-bar < $550)?

Referring to the statement above, the z-score for x-bar=$550 equals?
a. z(x-bar) = 0.5
b. z(x-bar) = - 2.5
c. z(x-bar) = -0.5
d. z(x-bar) = 0.25

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Answer #1

Given that mean  µ = 600

Standard deviation s = 100

sample n = 25

Probability that randomly selected graduates have an average weekly income of less than $550

P( X < 550)= P( Z < 550 - 600 / 100/ √25 )
= P( Z < -50/20)
= P( Z < -2.5)

. Hence z(x-bar) = - 2.5
The correct option is B

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