Statistics, standard deviation, mean, and z score

Question

the local police force gives all applicants an entrance exam and accepts only those applicants who score is the top 1.5% on teh test. Assuming the scores are normally distributed, the mean score is 85 points, the standard deviation is 12 points. what is the minimum score accepted?

Answer 1

Hello Ed,

Since the scores are assumed to be normally distributed, we should first find the z score that corresponds to the top 1.5% using a standard normal distribution table. The area to the left of the z-score we are looking for is 100% - 1.5% = 98.5% = 0.9850. From the table we find that the corresponding z-score is 2.07.

Remember that,

z = (x - μ)/σ ⇒ x - μ = z*σ ⇒ x = μ + z*σ

Hence, x = 85 + (2.07)*12 = 109.84

The minimum score accepted is 110 (assuming whole number scores).