Question

A population of values has a normal distribution with μ=168 and σ=47.2 You intend to draw a random sample of size n=43

Find the probability that a sample of size n=43 is randomly selected with a mean less than 173.
P(M < 173) =

Answer 1

Solution :

Given that ,

mean = = 168

standard deviation = = 47.2

n = 43

= = 168 and

= / n = 47.2 / 43 = 7.1979

P(M < 173) =   P((M - ) / < (173 - 168) / 7.1979)

= P(z < 0.69)   Using standard normal table.   

Probability = 0.7549