Question

Question #813cd

Answer 1

136, 171, and 220 pages, respectively.

Explanation:

If X is the number of pages read by the student, `X~N(mu=150,sigma=30)`
then at what C is

`P(X < C)=0.32`

`P(X < C)=0.32+0.43=0.77`

`P(X < C)=0.32+0.43+0.24=0.99`

You can find C for the standard normal case though tables (or by using Excel function NORMSINV(0.32)), then find X for `X~N(mu=150,sigma=30)` by multiplying by 30 and adding 150.

For example,
`if P(X < C)=0.32, C = NORMSINV(0.32) = -0.4677` for the standard normal case, and `-0.4677 * 30 + 150 = 136` (rounded up) for the `N(mu=150,sigma=30)` case.

Note if you're using Excel, you can use NORMINV(150, 30) to get the answer, but since this is probably for a class, it is useful to learn to convert to and from a standard normal distribution.