Question

You decide that accepting players within the top 2.5% height bracket will be reasonable for your team. Assume that the height of all people follows a normal distribution with a mean of 70.6 in and a standard deviation of 2.8 in. Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team. Give your answer in inches to the nearest inch.

Answer 1

Answer:

C=76 in (answer in inches to the nearest inch)

Explanation:

The statement of question tells us only 2.5% players to be taller than the cut off height C. It means 97.5% are smaller than the cut off height C. We first have to look in standardized normal distribution tables to find the corresponding value of 97.5% which is 1.96.

Now:

z=1.96

mean=μ=70.6

Standard deviation=σ=2.8

Formula:

$z=\frac{C-\mu}{\sigma} \\C=(z*\sigma)+\mu$

C=(1.96*2.8)+70.6

C=76.088 in

C=76 in (answer in inches to the nearest inch)