Question

For a certain population of patients with low hemoglobin levels, the mean is 11.5 grams/dl and standard deviation is 8 grams/dl. What is the probability that the mean hemoglobin level for a sample of 64 patients is between 9.5 grams/dl and 10.5 grams/dl?

Answer 1

Solution:

We have to find P(9.5<Xbar<10.5)

P(9.5<Xbar<10.5) = P(Xbar<10.5) – P(Xbar<9.5)

Find P(Xbar<10.5)

Z = (Xbar - µ)/[σ/sqrt(n)]

µ = 11.5

σ = 8

n = 64

Xbar = 10.5

Z = (10.5 – 11.5)/[8/sqrt(64)]

Z = -1

P(Z< -1) = P(Xbar<10.5) = 0.158655254

(by using z-table or excel)

Now find P(Xbar<9.5)

Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (9.5 – 11.5)/[8/sqrt(64)]

Z = -2

P(Z<-2) = P(Xbar<9.5) = 0.022750132

(by using z-table or excel)

P(9.5<Xbar<10.5) = P(Xbar<10.5) – P(Xbar<9.5)

P(9.5<Xbar<10.5) = 0.158655254 - 0.022750132

P(9.5<Xbar<10.5) = 0.135905122

Required probability = 0.1359