Mathematics: 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) =

Is this supposed to be True or False, if it is, answer is true....

Scores for a common standardized college aptitude

Ответ:

kingethan08

18.01.2022

Mathematics

Answer with explanation:

Let x denotes the score of a man.

As per given , we have

$\mu = 512\\\\ \sigma=106$

If 1 of the men is randomly selected, find the probability that his score is at least 559.5 will be :-

$P(X 559.5) =1- P(X\leq X)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{559.5-512}{106})\\\\=1-P(z\leq 0.448\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\ =1 - 0.6729= 0.3271$

Hence, the probability that his score is at least 559.5 is 0.3271 .

Let M be the sample mean.

$P(M 559.5) =1-P(M\leq 559.5)\\\ =1- P(\dfrac{M-\mu}{\dfrac{\sigma}{\sqrt{18}}}\leq\dfrac{559.5-512}{\dfrac{106}{\sqrt{18}}})\\\\ =1-P(z\leq1.90 )\ \ [ \because\ z=\dfrac{M-\mu}{\dfrac{\sigma}{\sqrt{18}}}]\\\\ =1-0.9713\\\\=0.0287$

Hence, if 18 of the men are randomly selected, find the probability that their mean score is at least 559.5 is 0.0287.

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