Answer:
0.9599 is the probability that a randomly selected running back has 64 or fewer rushing yards.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(running back has 64 or fewer rushing yards)
[tex]P( x \leq 64) = P( z \leq \displaystyle\frac{64 - 50}{8}) = P(z \leq 1.75)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x \leq 64) = 0.9599[/tex]
0.9599 is the probability that a randomly selected running back has 64 or fewer rushing yards.
