Question

A new manufacturing plant has 20 job openings. To select the best 20 applicants from among the 1,000 job seekers, the plant's personnel office administers a written aptitude test to all applicants. The average score on the aptitude test is 150 points with a standard deviation of 10 points. Assume the distribution of test scores is approximately mound-shaped.

What percentage of the test scores will fall between 130 and 160 points?

Answer 1

The mound shaped distribution will be the same as a normal distribution. The answer may use some "normal distribution online calculator", but in this case, as the points can be found to be away from the mean by 2 and 3 standard deviations away, we may use the following method.

As the distribution is a normal distribution, we may say that and . Also, as the distribution is symmetric, we have and . Hence, by putting the values, we have or , and or . Thus, or or .

Note: We may find a little bit different value in the online calculator, as the and is approxed to be 0.95 and 0.68 up to two decimals.