*. The time needed to complete a final examination in aparticular college course

Question

*. The time needed to complete a final examination in aparticular college course is    normally distributed witha mean of 80 minutes and a standard deviation of 10 minutes. Please answer the following questions.

a. What is the probability that a student will complete the examin more than 60 minutes but less than 75 minutes?__________

b. Assume that the class has 60 students and that theexamination period is 90 minutes in length. How many studentsdo you expect will be unable to complete the exam in theallotted time? __________

Explanation / Answer

a) P(60<x<75) z = (x-)/ z1 = (60-80)/10 = -2 z2 = (75-80)/10 = -0.5 P(60<x<75) = P(-2<z<-0.5) = normalcdf(-2,-0.5) =0.2858 probability that a student will complete the test in more than60 min but less than 75 min is 28.58% b)P(x<90) z = (90-80)/10 = 1 P(x<90) = P(z<1) = normalcdf(-100,1) = 0.8413 (0.8413)(60students) = 50.48 = 50 students will be able tocomplete the exam, so 10 students won't.

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