The time needed to complete a final examination in a particular college course i

Question

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions. a. What is the probability of completing the exam in one hour or less (to 4 decimals)? _______ b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? ________ c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to 2 decimals)? ___________

Explanation / Answer

Given, mean = 79 minutes, standard deviation, s = 8 minutes
Formula for standardised z score is, z = (x-mean)/s

a) P(X <= 60) = P(X < 60) = P(Z < (60-79)/8) = P(Z < -2.375) = 0.0088(from z table)

b) P(60 < X < 75) = P(X < 75) - P(X < 60) = P(Z < (75-79)/8) - P(Z < (60-79)/8) = P(Z < -0.5) - P(Z < -2.375)
= 0.3085 - 0.0088 = 0.2997

c) Lets find P(X > 90)
P(X > 90) = 1 - P(X < 90) = 1 - P(Z < (90-79)/8) = 1 - P(Z < 1.375) = 1 - 0.9154 = 0.0846, This is the proportion of students who will be unable to complete in the allotted time.
There are 60 students, therefore the number of students unable to finish in the allotted time is,
0.0846*60 = 5.076 = 5.08 students

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