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. If students have only 90 minutes to complete the exam, what percentage of the class will not finish the exam in time?

Answer 1

Hence total of 10 students are not able to complete the exam.

Explanation:

Given:

Mean for completing exam =80 min

standard deviation =10 min.

To find:

how much student will not complete the exam?

Solution:

using the Z-table score we can calculate the required probability.

Z=(Required time -mean)/standard deviation.

A standard on an avg class contains:

60 students.

consider for 70 mins and then 90 mins (generally calculate ± standard deviation of mean)(80-10 and 80+10).

1)70 min

Z=(70-80)/10

Z=-1

Now corresponding p will be

P(z=-1)

=0.1587

therefore

Now for required 90 min will be

Z=(90-80)/10

=10/10

z=1

So corresponding value of p is

P(z<1)=0.8413

this means 0.8413 of 60 students are able to complete the exam.

0.8413*60

=50.47

which approximate 50 students,

total number =60

and total number student will able to complete =50

Total number of student will not complete =60-50

=10.