Answer:
The percentage is [tex]P(X > 145 ) = 44.811\%[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 139[/tex]
The standard deviation is [tex]\sigma = 46[/tex]
The weight Scott can bench is x = 145 pounds
Generally the percentage of statisticians that can bench more than Scott is mathematically represented as
[tex]P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x- 139 }{46 } )[/tex]
=> [tex]P(X > 145 ) = P(\frac{X - \mu }{\sigma } > \frac{145 - 139 }{46 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(X > 145 ) = P(Z > 0.13043)[/tex]
From the z table
The area under the normal curve to the right corresponding to 0.13043 is
[tex]P(Z > 0.13043) = 0.44811[/tex]
=> [tex]P(X > 145 ) = 0.44811[/tex]
Converting to percentage
[tex]P(X > 145 ) = 0.44811 * 100[/tex]
=> [tex]P(X > 145 ) = 44.811\%[/tex]
