Question

Please show your work - the answer is d) but I'm not sure why. Thank you!

The time it takes to complete a Sta220 term test is normally distributed with a mean

of 100 minutes with standard deviation of 14 minutes. How much time should be

allowed if we wish to ensure that at least 9 out of 10 students (on average) can

complete it? (round to the nearest minute)

A) 115

B) 116

C) 117

D) 118

E) 119

Answer 1

Solution:

Given: The time it takes to complete a Stat220 term test is normally distributed with a mean of 100 minutes with standard deviation of 14 minutes.

That is:

We have to find x = Time , that should be allowed if we wish to ensure that at least 9 out of 10 students (on average) can complete it.

That is find x such that:

P( X < x ) = 9 /10

P( X < x ) = 0.90

Thus find z such that :

P( Z < z) = 0.9000

Look in z table for Area = 0.9000 or its closest area and find corresponding z value.

Area 0.8997 is closest to 0.9000 and it corresponds to z =1.2 and 0.08

Thus z = 1.28

Now use following formula to find x value using z value.

Thus correct option is: D. 118