Question

You are the coach of a basketball team that is currently looking for new players. One of the criteria for selection as a player is that the person must be above a particular height. Ideally, you want your next player to be as tall as possible. However, you do not want to rule out any potential players by making the cut-off height too strict. 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 69 in and a standard deviation of 2.9 in. Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team. you may find this standard normal table useful. Give your answer in inches to the nearest inch.
C= _____ in

Answer 1

Answer:

C = 75 in

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Assume that the height of all people follows a normal distribution with a mean of 69 in and a standard deviation of 2.9 in.

This means that $\mu = 69, \sigma = 2.9$

Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team.

This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975, so X when Z = 1.96.

$Z = \frac{X - \mu}{\sigma}$

$1.96 = \frac{X - 69}{2.9}$

$X - 69 = 1.96*2.9$

$X = 74.7$

Rounded to the nearest inch,

C = 75 in