Central Limit Theorem 5.0

Question

A population of values has a normal distribution with  and . You intend to draw a random sample of size .

Find the probability that a sample of size  is randomly selected with a mean less than 173.3.P(M < 173.3) =

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

Standardize the normal random variable.

z = (x - µ) / (σ / √n)

z = (173.3 - 180.3) / (46 / √174)

z = -2.00

If we find the probability using a z-score of +2.00, we can subtract it from 1 to find the probability the mean is less than a z-score of -2.00.

For a z-score of 2.00, the probability is .9772

1 - .9772 = .0228 or 2.28%