6. The Air Force measures reaction times of candidates for flight school. Over t

Question

6. The Air Force measures reaction times of candidates for flight school. Over the last several years, reaction times have been normally distributed with a mean of 1.31 seconds and a standard deviation of 0.31 seconds. The maximum allowable reaction time for admittance into flight school is 1.59 seconds.

a. What is the z-score of a candidate with a reaction time of 1.59 seconds?
b. What percent of all applicants will have a reaction time is greater than 1.59 seconds and thus be rejected?
c. What is the reaction time that separates the fastest 14% of the candidates from the rest of the candidates?

Explanation / Answer

Given X~Normal(=1.31,s=0.31)

(a) the z-score is (x-)/s = (1.59-1.31)/0.31 = 0.90

(b) P(X>1.59)= P(Z>0.9)=1-P(Z<=0.9)= 0.1841 (check normal table)

(c) P(X>c)=0.14

--> P(X<=c) = 1-0.14 =0.86

--> P(Z<= (c-1.31)/0.31) = 0.86

--> (c-1.31)/0.31 = 1.08

--> c= 1.31 + 0.31*1.08 = 1.6448

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