Question

 

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

(a)

What is the probability of completing the exam in one hour or less? (Round your answer to four decimal places.)

(b)

What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (Round your answer to four decimal places.)

(c)

Assume that the class has 80 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? (Round your answer up to the nearest integer.)

students

Answer 1

Here the variable of interest is thetime require to complete a final exam in a particular college. Let X represents the time require to complete a final exam in a particular college days expressed in minutes. If X is normal distributed then its probability density function is given by

For mean of 80 and standard deviation 10, we have

a) The probability of completing the exam in less than one hour is obtained by considering X<60 , as X is measure in minute and the require probability is given by

Now, we make use of some property for obtaining the probability

1. P(Z<-a)=P(Z>a)

2. P(-a

3.P(Z>c)=0.5-P(0

Therefore, we have

b) The probability for student completing the exam in more than 60 but less than 75 minutes is P(60

c) In this case we have to obtain the number of students unable to complete the exam if the student allotted time is 90 minutes. If the students are unable to complete the exam it means their completion time is more than 90 minutes. Now, we obtain the probability for X>90 and the required probability can be obtained by making use of probability table which is given below

The probability of student unable to complete the exam is 0.1587 and there are total 80 students in the class so the number of students unable to complete the exam is given by

=80*P(X>90)=80*0.1587=12.696.

Therefore on roundoff, we get 13 students unable to complete the exam .