Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 492...

Scores for a common standardized college aptitude test are normally distributed with a mean of 492 and a standard deviation of 100. 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 533.3. P(X > 533.3) = ?

NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If 15 of the men are randomly selected, find the probability that their mean score is at least 533.3. P(M > 533.3) = ?

NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If the random sample of 15 men does result in a mean score of 533.3, is there strong evidence to support the claim that the course is actually effective?

No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 533.3.

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 533.3.

1)

If 1 of the men is randomly selected, find the probability that his score is at least 533.3. :

 probability =P(X>533.3)=P(Z>(533.3-492)/100)=P(Z>0.41)=1-P(Z<0.41)=1-0.6602=0.3398

2)

 sample size       =n= 15 std error=σx̅=σ/√n= 25.8199

If 15 of the men are randomly selected, find the probability that their mean score is at least 533.3 :

 probability =P(X>533.3)=P(Z>(533.3-492)/25.82)=P(Z>1.6)=1-P(Z<1.6)=1-0.9451=0.0549

3)

o. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 533.3.

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