Question

A population of values has a normal distribution with μ=180.3μ=180.3 and σ=46σ=46. You intend to draw a random sample of size n=174n=174.

Find the probability that a sample of size n=174n=174 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

= 180.3

= 46

n = 174

SE = /

= 46/

= 3.4873

To find P( < 173.3):

Z = (173.3 - 180.3)/3.4873

= - 2.0073

By Technology, Cumulative Area Under Standard Normal Curve = 0.0224

So,

P( < 173.3):= 0.0224

So,

Answer is:

0.0224