Question

Scores of the Math portion of the SAT (SAT-M) are known to have a national mean μ=500 and standard deviation σ=100. A random sample of n=400 high-school seniors was chosen and their average SAT-M score was found to be x̅=522. Would this finding surprise you?

A, Yes, since an average of 522 is more than 4 standard deviations above 500.

B. Yes, since an average of 522 is larger than 500.

C. No since an average of 522 is less than one standard deviation above 500

D. No, since we are not told that SAT-M scores have a normal distribution in the population.

E. Yes, since an average of 522 is larger than 500 and the sample size (n=400)

is large enough.

Answer 1

By Central Limit Theorem,

Mean of sampling distribution of mean = 500

Standard deviation of sampling distribution of mean, standard error =

=

= 5

Z score of 522 = (522 - mean)/standard error

= (522 - 500)/5

= 4.4

522 is 4.4 standard deviation above 500

A value is unusual if its is more than 2 standard deviations away from mean

The value of 522 is unusual and hence, surprising

A) Yes, since an average of 522 is more than 4 standard deviations above 500.