Question

The mean score for freshmen on an aptitude test at a certain college is 530 ​, with a standard deviation of 50 . Assume the means to be measured to any degree of accuracy. What is the probability that two groups selected at​ random, consisting of 54 and 50 ​students, respectively, will differ in their mean scores by

​(a) more than 11 ​points? ​

(b) an amount between 2 and 8 ​points?

​(a) The probability the difference is more than 11 points is ___ . ​(Round to four decimal places as​ needed.) ​

(b) The probability the difference is between 2 and 8 points is ___ . ​(Round to four decimal places as​ needed.)

Answer 1

Answer:

Given,

Mean = 530

Standard deviation = 50

u1 - u2 = 0

standard deviation = 50*sqrt(1/54 + 1/50) = 9.8131

a)

P(|x1-x2| > 11) = 2P(z < - 11/9.8131)

= 2P(z < - 1.121)

= 0.2622879 [since from z table]

= 0.2623

b)

P(-8 < (x1-x2) < -2) + P(2 < (x1-x2) < 8) = 2P(2 < z < 8)

= 2P(2/9.8131 < z < 8/9.8131)

= 2P(0.2038 < z < 0.8152)

= 2[P(z < 0.8152) - P(z < 0.2038)]

= 2[0.7925211 - 0.5807451] [since from z table]

= 0.4236