Math CentralQuandaries & Queries


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?


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

standard normal conversion                  (1)

For part b) find

standard normal conversion

and use you standard normal table to find

Pr(Z ≥Zo)

For part a) find Zc so that

Pr(Z ≥ Zc) = 0.15

and then use

standard normal conversion

to find the cut-off score Xc.


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