Question

The time needed to complete a final examination in a particular college course is normally distributed...

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 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? (Round your answer up to the nearest integer.)

#=80

=10

a)probability to complete it with in one hour =P(X<60)

=P((x-)/<(60-80)/10)

=P(Z<-2)

#Value of z is obtain from standard normal table

=0.0228

b)

P(60<X<75)=P((60-80)/10<(x-)/<(75-80)/10)

=P(-2<Z<-0.5)

=P(Z<-0.5)-P(Z<-2)

=0.3085-0.0228

=0.2858

c)

P(X>90)=P((x-)/>(90-80)/10)

=P(Z>1)

=0.1587

hence number of students =np=60*0.1587 =~10