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

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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.