Student scores on exams given by a certain instructor have m

Student scores on exams given by a certain instructor have mean 74 and standart deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class size 64

a)approximate the probability that the average test score in the class of 25 exceeds 80

b)repeat for class size 64

c)approximate the probabilty that the avarage test score in the larger class exceed s that of the other class by over 2.2 points.

Solution

We assume normal distribution.

Thus,

a) For class of 25

P ( X > 74) = P (Z > 80 - 74/ 14/sqrt(25) )

= P (Z < 6 / 2.8)

= P ( Z < 2.14)

= 0.9838

P ( Z > 2.14) = 1- 0.9838

= 0.0162

b)

Similarly:

For class of 64

P ( X > 74) = P (Z > 80 - 74/ 14/sqrt(64) )

= P (Z < 6 / 1.75)

= P ( Z < 3.428)

= 0.9838

P ( Z > 2.14) = 1- 0.9997

= 0.0003

c) Probability of the difference exceeding 2.2

= P (Z > 2.2 / sqrt [ 14 * {(1/25) + (1/64)} ]

= P (Z > 2.49)

= 0.9936

P (Z < 2.49)

= 1 - 0.9936

= 0.0064

Hope this helps.