Question

Suppose that ? is normally distributed with mean 90 and standard deviation 11.

A. What is the probability that ? is greater than 109.25?

B. What value of ? does only the top 15% exceed?

Answer 1

Zscore normal distribution formula:

z = (x - μ) / σ

A. What is the probability that ? is greater than 109.25?

Z = (109.25-90)/11 = 1.75

Answer: P(Z > 1.75) = 0.0401

B. What value of ? does only the top 15% exceed?

Excel formula:

=NORMSINV(1-0.15)*11+90

= 101.40

Value of ? does only the top 15% exceed is 101.40

Another way of calculating using z score:

The z-score that corresponds to the top 15% (which would mean a right-tail area equal to 0.15) is z = 1.036

=90+1.036*11

=101.40