SOLUTION: The heights of applicants to the police force are normally distributed with mean 170 cm and standard deviation 3.8 cm. If 30% applicants are rejected on account of their low height

Question 1172479: The heights of applicants to the police force are normally distributed with mean 170 cm and standard deviation 3.8 cm. If 30% applicants are rejected on account of their low height. What is the minimum acceptable height for the police force?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 170 cm.
standard deviation is 3.8 cm.
30% are rejected.
minimal height is 168.007 cm.
anybody shorter than that is rejected.
i used the following calculator to find this.
http://davidmlane.com/hyperstat/z_table.html
here's a display of the results.

if you had to use the z-score tables you would do the following.
look for an area to the left of the z-score that is closest to .30
i round:
.30153 associated with a z-score of -.52
.29806 associated with a z-score of -.53.
the difference between the two z-scores is .01
the difference between the two areas is .00347
the difference between .30153 and .3 is .00153.
.00153 / .00347 = x / .01
solve for x to get:
x = .0044092219.
subtract this from -.52 to get -.5244092219.
in the z-score formula of:
z = (x - m) / s
z = -.5244092219
m = 170
s = 3.8
solve for x to get:
x = 3.8 * -.5244092219 + 170 = 168.007245.
that 's very close to what the calculator told me.
that's your solution.

RELATED QUESTIONS
The heights of applicants to the police force are normally distributed with mean 170 cm... (answered by Boreal)

Suppose that people's heights (in centimeters) are normally distributed, with a mean of... (answered by stanbon)

Suppose that people's heights (in centimeters) are normally distributed, with a mean of... (answered by ewatrrr)

The heights of a certain species of plant are normally distributed, with mean 22 cm and... (answered by Fombitz)

. Edna Crabapple is 170 cm tall. If the heights of her students are distributed... (answered by ikleyn)

Suppose that people's heights (in centimeters) are normally distributed, with a mean of... (answered by stanbon)

Suppose that people's heights (in centimeters) are normally distributed, with a mean of... (answered by Theo)

In order to qualify for a police academy, applicants are given a test of physical... (answered by Boreal)