Question

The overhead reach distances of adult female are normally distributed with a mean (µ ) of 202.5cm and standard deviation (Ơ ) of 8.2 cm. Find the probability that the mean for 25 sample randomly selected distances is less than 200.20 cm

Answer 1

= 202.5, = 8.2, n= 25

We want to find P(x < 200.20)

formula for z-score is

z = −1.4024

z = −1.40

P(x < 200.20) = 1 - P(z < -1.40)

using z table we get

P(z < -1.40)= 0.0804

P(x < 200.20) = 0.0804

Probability = 0.0804

Probability of the mean for 25 sample randomly selected distances is less than 200.20 cm is = 0.0804