Difficult Math Question

Question

The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top 10% on this test. If the mean score this year is 89 and the standard deviation is 8, what is the minimum score an applicant would need to earn to be accepted?

Answer 1

z score = (x-89)/8= 1.282

x-89= 10.256

x=99.256

by the empirical rule top 5% would be found with a z score of 2

x-89 =8(2)= 16

x = 105

if 100 is the maximum score, this suggests the normal distribution is not a good fit for the test scores

it's not a symmetrical distribution

find the z score for 10% by using a z calculator or z tables. z=1.282 standard deviations above the mean