Question

Student scores on exams given by a certain instruc-tor have mean 74 and standard deviation 14. Thisinstructor is about to give two exams, one to a classof size 25 and the other to a class of size 64.(a)Approximate the probability that the averagetest score in the class of size 25 exceeds 80.(b)Repeat part (a) for the class of size 64.(c)Approximate the probability that the averagetest score in the larger class exceeds that ofthe other class by over 2.2 points.(d)Approximate the probability that the averagetest score in the smaller class exceeds that ofthe other class by over 2.2 points.

Answer 1

Explanation:

Given that Student scores on exams given by a certain instruc-tor have mean 74 and standard deviation 14.

Group I X Group II Y

Sample mean 74 74

n 25 64

Std error (14/sqrtn) 2.8 1.75

a) P(X>80) =
`1-0.9839\\= 0.0161`

b) P(Y>80) =
`1-0.9997\\=0.0003`

c) X-Y is Normal with mean = 0 and std deviation =
`√(2.8^2+1.75^2) \\=3.302`

P(X-Y>2.2) =
`1-0.8411\\=0.1589`

d)
`P(\bar x -\bar Y>2.2) = 0.1589`