Mathematics, 05.02.2020 21:42, OoofIamdead
Scores for a common standardized college aptitude test are normally distributed with a mean of 512 and a standard deviation of 106. randomly selected men are given a test preparation course before taking this test. assume, for sake of argument, that the test has no effect
if 1 of the men is randomly selected, find the probability that his score is at least 559.5.
p(x > 559.5) =
if 18 of the men are randomly selected, find the probability that their mean score is at least 559.5.
p(m > 559.5) =
Answers: 1
![P(X 559.5) =1- P(X\leq X)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{559.5-512}{106})\\\\=1-P(z\leq 0.448\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\ =1 - 0.6729= 0.3271](/tpl/images/0504/1333/84e75.png)
![P(M 559.5) =1-P(M\leq 559.5)\\\ =1- P(\dfrac{M-\mu}{\dfrac{\sigma}{\sqrt{18}}}\leq\dfrac{559.5-512}{\dfrac{106}{\sqrt{18}}})\\\\ =1-P(z\leq1.90 )\ \ [ \because\ z=\dfrac{M-\mu}{\dfrac{\sigma}{\sqrt{18}}}]\\\\ =1-0.9713\\\\=0.0287](/tpl/images/0504/1333/5eae0.png)
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Scores for a common standardized college aptitude test are normally distributed with a mean of 512 a...
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