Question

A normal population has a mean of 12.2 and a standard deviation of 2.5. compute the z value associated with 14.3. what proportion of the population is between 12.2 and 14.3? what proportion of the population is less than 10.0?

Answer 1

The z-score associated with 14.3 is 0.84.  0.2995 of the population is between 12.2 and 14.3.  0.1894 of the population is less than 10.0.

The formula for a z-score is

z=(X-μ)/σ

With our data, we have:
z=(14.3-12.2)/2.5=0.84

The z-score associated with the mean is 0.5.  To find the proportion of the population between the mean and 14.3, subtract 0.7995 (the proportion of population below the z-score of 0.84, using http://www.z-table.com) and 0.5:

0.7995 - 0.5 = 0.2995.

The z-score for 10.0 is

(10.0-12.2)/2.5 = -0.88.  The proportion of the population less than this is 0.1894.