In: Statistics and Probability
33. The College Board reports that the in 2016, the mean mathematics SAT score was 515, and the standard deviation was 116. A sample of 65 scores is chosen from the population of all SAT scores. Find the probability that the sample mean score is less than 500.
(a) .1492 (b).8508 (c) -.13 (d) .4483 (e) .5517
36. Refer to question 33. Would it be unusual if the sample mean were greater than 550?
(a) No (b) Yes
Solution:
Given that,
n = 65
= ( /n) = (116 / 65 ) = 14.3880
= P ( - /) < (500 - 515 / 10.3880 )
= P ( z < - 15 / 10.3880 )
= P ( z < -1.04 )
Using z table
= 0.1492
Probability = 0.1492
= 1 - P ( - /) < (550 - 515 / 10.3880 )
= 1 - P ( z < 35 / 10.3880 )
= 1 - P ( z < 2.43 )
Using z table
= 1 - 0.9925
= 0.0075
Probability = 0.0075
Probability < 0.05 Sample mean is unusual Yes
Answer b) is correct.