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 586.

(b)  If 10 men are randomly selected, find the probability that their mean score is at least 586.

(c) 10 randomly selected men were given a review course before taking the SAT test. If their mean score is 586, is there a strong evidence to support the claim that the course is actually effective?
(Enter YES or NO)

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 509

S.d = 112

A)

P(x>586)

Z = 586-509)/112 = 0.69

From z table, P(z>0.69) = 0.2451

B)

In case of sample

Z = (x - mean)/(s.d/√n)

Z = (586 - 509)/(112/√10) = 2.17

From z table, P(z>2.17) = 0.015

C)

Null hypothesis Ho : u = 509

Alternate hypothesis Ha : u > 509

As the probability obtained for being greater than 586 is 0.015 which is less than 0.05

We reject the null hypothesis

So, yes there a strong evidence to support the claim that the course is actually effective