Candidates for employment at a city fire department are required to take a writt

Question

Candidates for employment at a city fire department are required to take a
written aptitude test. Scores on this test are normally distributed with mean 280 and
standard deviation 60. A random sample of nine test scores was taken.

a. What is the standard error of the sample mean score?

b. What is the probability that the sample mean score is less than 270?

c. What is the probability that the sample mean score is more than 250?

d. Suppose that the population standard deviation is in fact 40 rather than 60.
Without doing the calculations, state how this would change your answers to a, b and c?

Explanation / Answer

= 280 = 60 n = 9

a. Standard error = / n

= 60 / 9

= 60 / 3

= 20.

b. P(x' < 270)

= P(z < (270 - 280) / 60 * 9)

= P(z < -0.5)

= 0.3085.

c. P(x' > 250)

= P(z > (250 - 280) / 60 * 9)

= P(z > -1.5)

= 0.9332.

d. If the standard deviation changes to 40 instead of 60, the standard error increases (becomes 3/2 of the initial value).

The probability decreases in part b while it increases in part c.

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