How did we get 85.89 and 0.1235 using a calculator to get the correct answer? Thanks!
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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How did we get 85.89 and 0.1235 using a calculator to get the correct answer? Thanks!

Transcribed Image Text:The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal
with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a
certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the
probability that the volunteer selected will receive a certificate of merit given that the number of hours the
volunteer worked is less than 90 ?
(A) 0.077
(B) 0.123
(C) 0.134
(D) 0.618
(E) 0.923

Transcribed Image Text:(C)
Correct. If X represents the number of hours worked, then the
value of X for which 20 percent of the hours worked are greater
than X in a normal distribution with mean 80 and standard
deviation 7 can be found using technology to be approximately
85.89. Then the probability that the volunteer selected will receive a
certificate of merit given that the number of hours the volunteer
worked is less than 90 is given by
P(X > 85.89 | X < 90) =
P(85.89 < X < 90)
P(X < 90)
Technology can be
used to find that P(85.89 < X <90) ≈ 0.1235 and that
P(X<90) ≈ 0.924 in a normal distribution with mean 80 and
standard deviation 7, so
P(X > 85.89 | X < 90) =
P(85.89 < X < 90)
P(X <90)
0.1235
0.9234
≈ 0.134.
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