Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 499 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 557.2. P(X > 557.2) = 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 9 of the men are randomly selected, find the probability that their mean score is at least 557.2. P(M > 557.2) = 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

It is given that mean = 499 and standard deviation = 97

(A) P(more than 557.2)

using normalcdf(lower bound, upper bound, mean, standard deviation)

setting lower bound = 557.2, upper bound = infinity or E99, mean = 499 and standard deviation = 97

= normalcdf(557.2,E99,499,97)

= 0.2743 (rounded to 4 decimals)

(B) P(more than 557.2 for a sample of 9)

using normalcdf(lower bound, upper bound, mean, standard deviation)

setting lower bound = 557.2, upper bound = infinity or E99, mean = 499 and standard deviation = 97/sqrt{9}

= 97/3

= 32.33

setting the values, we get

= normalcdf(557.2,E99,499,32.33)

= 0.0359(rounded to 4 decimals)