A normal distribution problem

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Question from EDGAR, a student:

to qualify for security officers training recruits are tested for stress tolerance. The scores are normally distributed with mean of 62 and a standard deviation of 8.
a.) If only the top 15% of recruits are selected, find the cutoff score
b.) If a candidate is randomly selected, what is the probability that his or her socre is at least 55?

Edgar,

First you need to convert the normal random variable X with mean μ = 62 and standard deviation σ = 8 to the standard normal random variable Z using

(1)

For part b) find

and use you standard normal table to find

Pr(Z ≥Z_o)

For part a) find Z_c so that

Pr(Z ≥ Z_c) = 0.15

and then use

to find the cut-off score X_c.

Harley

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