Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 514 and a standard deviation of 97. 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 555.2.
P(X > 555.2) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If 16 of the men are randomly selected, find the probability that their mean score is at least 555.2.
P(M > 555.2) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given that ,

mean = = 514

standard deviation = = 97

a) P(x > 555.2) = 1 - p( x< 555.2)

=1- p P[(x - ) / < (555.2 - 514) / 97 ]

=1- P(z < 0.425)

Using z table,

= 1 - 0.6646

= 0.3354

b) n = 16

=   = 514

= / n = 97 / 16 = 24.25

P(M > 555.2) = 1 - P(M < 555.2)

= 1 - P[(M - ) / < (555.2 - 514) / 24.25]

= 1 - P(z < 1.699)

Using z table,    

= 1 - 0.9553

= 0.0447