Question

From a population of 10,000 students, an average height of
174.5 cm and a standard deviation of 6.9 cm. A sample of 50 is drawn
students. What is the expected number of students in the sample whose
height varies between 173 cm and 175 cm?

Answer 1

Solution:

We are given

n = 50

µ = 174.5

σ = 6.9

First we have to find P(173<Xbar<175)

P(173<Xbar<175) = P(Xbar<175) - P(Xbar<173)

Find P(Xbar<175)

Z = (Xbar - µ)/(σ/sqrt(n))

Z = (175 - 174.5)/(6.9/sqrt(50))

Z = 0.512396

P(Z<0.512396) = P(Xbar<175) = 0.695813

(by using z-table)

Now find P(Xbar<173)

Z = (Xbar - µ)/(σ/sqrt(n))

Z = (173 - 174.5)/(6.9/sqrt(50))

Z =-1.53719

P(Z<-1.53719) = P(Xbar<173) = 0.062124

(by using z-table)

P(173<Xbar<175) = P(Xbar<175) - P(Xbar<173)

P(173<Xbar<175) = 0.695813 - 0.062124

P(173<Xbar<175) = 0.633689

Expected number of students = n* P(173<Xbar<175) = 50*0.633689 = 31.68445

The expected number of students in the sample is Approximately 32 students whose height varies between 173 cm and 175 cm.