Question

Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112.
(a)  If 1 man is randomly selected, find the probability that his score is at least 585.

(b)  If 16 men are randomly selected, find the probability that their mean score is at least 585.

16 randomly selected men were given a review course before taking the SAT test. If their mean score is 585, is there strong evidence to support the claim that the course is actually effective?
(Enter YES or NO)  

Answer 1

Solution :

Given that,

mean = = 509

standard deviation = = 112.

a ) P (x > 585)

= 1 - P (x < 585 )

= 1 - P ( x -  / ) < ( 585 - 509 / 112.)

= 1 - P ( z < 76 / 112.)

= 1 - P ( z < 0.68 )

Using z table

= 1 - 0.7517

= 0.2483

Probability = 0.2483

b ) n = 16

=509

= / n = 112 16 = 28

P ( > 585)

= 1 - P ( < 585 )

= 1 - P ( - / ) < ( 585 - 509 / 28.)

= 1 - P ( z < 76 / 28.)

= 1 - P ( z < 2.71 )

Using z table

= 1 - 0.9966

= 0.0034

Probability = 0.0034

No

16 randomly selected men were given a review course before taking the SAT test. If their mean score is 585, is there strong evidence to support the claim that the course is actually effective