Question

Question 1 :

The population mean annual salary for chefs is $59,100, with a standard deviation of $1700. A random sample of 25 chefs is selected from this population. Find the probability that the mean annual salary of the sample is less than $55,000.

Question 2:

Suppose female student heights are normally distributed, with mean 66 inches and standard deviation 2 inches. Find the 95th percentile of female student heights, that is, the height X that is larger than 95% of all female student heights.

Answer 1

Question 1)

Given,

= 59100, = 1700

The central limit theorem is

P( < x) = P( Z < x - / / sqrt(n) )

so,

P( < 55000) = P( Z < 55000 - 59100 / 1700 / sqrt(25) )

= P( Z < -12.06)

= 0

b)

= 66, = 2.

95th percentile = + Z *

Where Z is critical value at 95% confidence.

95th percentile = 66 + 1.645 * 2

= 69.29