Question #813cd

1 Answer
statmango
Nov 10, 2016

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.

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