A random sample of size 36 is taken from a population with m

A random sample of size 36 is taken from a population with mean u = 17 and standard deviation of 6. What is the probability that the sample mean is greater than A) 18? B) Less than 5? C) Between 10 and 12?

Solution

N = 36

MEAN = 17

S.D = 6

A) P(GREATER THAN 18) =

For x = 18, the z-value z = (18 - 17) /6 = 1/6 = 0.166

Hence P(x > 18) = P(z < 2.5) = [area to the RIGHT of 0.166] = 0.5636

B)

For x = 5, the z-value z = (5 - 17) / 6 = -2

Hence P(x < 5) = P(z < -2) = [area to the left of 2.5] = 0.0183

C)