Question

The average score on a standardized test is 423 with a standard deviation of 21. The probability that a student will score above a 400 is​ 86.33%. In a group of 50 students who take this​ test, what is the probability that 40 or more score above a​ 400?

Answer 1

Solution:

For the given scenario, we are given

n = 50

p = 0.8633

q = 1 - 0.8633 = 0.1367

Mean = np = 50*0.8633 = 43.165

SD = sqrt(npq) = sqrt(50*0.8633*0.1367) = 2.429126

We have to find P(X≥40) = P(X>39.5) (continuity correction)

P(X>39.5) = 1 - P(X<39.5)

Z = (X - mean)/SD

Z = (39.5 - 43.165)/ 2.429126

Z = -1.50877

P(Z<-1.50877) = P(X<39.5) = 0.065678

(by using z-table)

P(X>39.5) = 1 - P(X<39.5)

P(X>39.5) = 1 - 0.065678

P(X>39.5) = 0.934322

Required probability = 0.934322