Question

1.

Scores for a common standardized college aptitude test are normally distributed with a mean of 485 and a standard deviation of 114. Randomly selected men are given a Test Prepartion 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 536. P(X> 536) = Round to 4 decimal places. If 20 of the men are randomly selected, find the probability that their mean score is at least 536. P(X > 536) = Round to 4 decimal places. If the random sample of 20 men does result in a mean score of 536, is there strong evidence to support the claim that the course is actually effective? O Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 536. O No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 536.

2.

Answer 1

scores for college aptitude test common standardized ca are normally distributed with a mean of 485 and a standard deviation of 114. is randomly selected, the probability that his score is atleast will be, PL x >536) -|- Pl * £ 536) = 1-p of the men of 536 ۴ ( Z L 536-485 114 = 1- Plz 0.44736 -1- 0 -673 = 0.3270 0.3270. So the probability is are men of 20 sandonly selected, then the sample means will be of the 20 of the sampling distribution X~~( 48s, 114 مدل

is atleast pl Z Ļ536-485 114 0.0230 The probability that their mean score is 536 will be, Š >536) = 1-pl P( X 2536 =1-11 jo 21-P 24 2.000 = 1- 0.977 to the probability a random sample of 20 men results in a mean score of 536, there is a strong evidence to support the claim that the course is actually effective because the probability indicates that it is that randomly selected group as 536. So the first option high hould cornect, is 0.0230. 9 I a highly unlikely of students Bay chance a a mlan as get is