Question

Bryce reads in the latest issue of Pigskin Roundup that the average number of rushing yards per game by NCAA Division II starting running backs is 50 with a standard deviation of 8 yards. If the number of yards per game (X) is normally distributed, what is the probability that a randomly selected running back has 64 or fewer rushing yards

Answer 1

0.9599 is the probability that a randomly selected running back has 64 or fewer rushing yards.

Explanation:

We are given the following information in the question:

Mean, μ = 50

Standard Deviation, σ = 8

We are given that the distribution of number of rushing yards per game is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(running back has 64 or fewer rushing yards)

`P( x \leq 64) = P( z \leq \displaystyle(64 - 50)/(8)) = P(z \leq 1.75)`

Calculation the value from standard normal z table, we have,

`P(x \leq 64) = 0.9599`

0.9599 is the probability that a randomly selected running back has 64 or fewer rushing yards.