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 Question from jude, a student: (1) Assuming that the heights of boys in high school basketball are normally distributed with a mean of 70 inches and a std dev. of 2.5 inches, how many boys in a group of 100 are expected to be 75 inches tall. 2) Past records from a bank show that the probability of being approved in the written application for hire is 0.63. Then the probability of being approved by the interview committee is 0.85, given that the candidate has been approved on the written application. What is the probability that a person will be approved on both the written application and the interview?

Jude,

1. This depends on how the question is to be interpreted. Do you mean:
(A) exactly 75.00000" tall [answer, none, they'll all be at least a little taller or shorter]

(B) 75" tall or more [answer, express this in terms of standard
deviations above the mean, and use a Z table or known "landmarks" of the normal curve. For example, 72.5" is one SD above the mean and about 1/6 (more accurately, 0.1587) of a normally distributed population are at least that large; so about 16 boys would be above 72.5" tall]

(C) how many would give their height as 75" to the nearest inch?
[Do the calculation above for 74.5" and 75.5" and subtract.]

2. Mental Trick 1: Think of this as proportions! If 63/100 of the candidates get an interview and 85/100 of those who get an interview are hired, what proportion are hired?

Mental Trick 2: If you still don't have a feel for this, try with easier numbers. If a third of the candidates for another job get an interview and half those get hired, what proportion are hired? Think of what you did, and now do the same with the other numbers.

Good Hunting!
RD

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