Question

The population of NBA players is Normally distributed

Answer 1

Using the normal distribution, it is found that:

1. 85% of NBA players are taller than Greg.

2. 15% are shorter.

3. A height of 6'11'' would be needed.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

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

• It 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, which is the percentile of X.

In this problem:

• In inches, considering that a feet has 12 inches, the mean is of $\mu = 6 \times 12 + 7 = 79$.

• The standard deviation is of $\sigma = 3.9$.

• Greg is 6'3'', that is, X = 6 x 12 + 3 = 75.

Item 1:

The proportion is one subtracted by the p-value of Z, hence:

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

$Z = \frac{75 - 79}{3.9}$

$Z = -1.03$

$Z = -1.03$ has a p-value of 0.15

1 - 0.15 = 0.85.

85% of NBA players are taller than Greg.

Item 2:

100 - 85 = 15% are shorter.

Item 3:

This is X when Z has a p-value of 1 - 0.025 = 0.975, so X when Z = 1.96.

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

$1.96 = \frac{X - 75}{3.9}$

$X - 75 = 1.96(3.9)$

$X = 83$

83 = 6 x 12 + 11.

A height of 6'11'' would be needed.

More can be learned about the normal distribution at brainly.com/question/24663213