Question

Apply the Central Limit Theorem for Sample Means

A population of values has a normal distribution with μ=77 and σ=9.2. You intend to draw a random sample of size n=30.

Find the probability that a sample of size n=30n=30 is randomly selected with a mean less than 76.8.

P(M < 76.8) =

Enter your answers as numbers accurate to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given that ,

mean = = 77

standard deviation = = 9.2

n = 30

M = = 77 and

M = / n = 9.2 / 30 = 1.6797

P(M < 76.8) =   P((M - M ) / M < (76.8 - 77) / 1.6797)

= P(z < -0.119)   Using standard normal table.   

Probability = 0.4526