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 agoRelated Solutions
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