Question

1. the heights of nfl football players are approximately normally distributed with a mean of 71.5 inches and a standard deviation of 2.3 inches. brock purdy is 6 feet 1 inches (74 inches) tall. what percentile does that place him at? (a) 43rd (b) 50th (c) 74th (d) 86th (e) 94th

Explanation:

Step1: Calculate z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 74$ (Brock Purdy's height), $\mu=71.5$ (mean height) and $\sigma = 2.3$ (standard deviation). So, $z=\frac{74 - 71.5}{2.3}=\frac{2.5}{2.3}\approx1.09$.

Step2: Find the percentile

We use the standard normal distribution table (z - table). Looking up the value of $z = 1.09$ in the z - table, the corresponding cumulative probability is approximately $0.8621$. This means Brock Purdy is at the approximately 86th percentile.

Answer:

D. 86th