Question

In: Statistics and Probability

typical student has a normal distribution with mean of 10 minutes and standard deviation of 2...

typical student has a normal distribution with mean of 10 minutes and standard deviation of 2 minutes to complete a question. The total exam has 80 minutes.

how many questions should the exam have so that only 6 in 10,000 students failed the exam?

(that is, p(y>80) = 0.0005)

Solutions

Expert Solution

y=time in minutes for exam

if no. of questions = n

sampling standard deviation = SD/(n^0.5)

table for P(z>Z) :

P(z>Z) = 0.0005

P(z<Z) = 1 - 0.0005 = 0.9995

Z = 3.3 from table above

mean time = 10 + 3.3*SD/(n^0.5)

total time = 80 min

[ 10 + 3.3*SD/(n^0.5) ] * n < 80

10*n + 6.6*(n^0.5) < 80

nearest integer n = 6

therefore exam should have 6 questions

(please UPVOTE)

orchestra answered 1 year ago
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