Question

How many pounds a statistician can bench press is normally distributed with a mean of 139 and standard deviation of 46. If Scott can bench 145 pounds, approximately what percentage of statisticians can bench more than Scott

Answer 1

Answer:

The percentage is  $P(X > 145 ) = 44.811\%$

Step-by-step explanation:

From the question we are told that

   The  mean is  $\mu = 139$

   The standard deviation is  $\sigma = 46$

   The weight Scott can bench is  x =  145 pounds

Generally the percentage of statisticians that can bench more than Scott is mathematically represented as

      $P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x- 139 }{46 } )$

 =>  $P(X > 145 ) = P(\frac{X - \mu }{\sigma } > \frac{145 - 139 }{46 } )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

    $P(X > 145 ) = P(Z > 0.13043)$

From the z table  

The area under the normal curve to the right corresponding to 0.13043  is  

     $P(Z > 0.13043) = 0.44811$

=>  $P(X > 145 ) = 0.44811$

Converting to percentage

     $P(X > 145 ) = 0.44811 * 100$

=>  $P(X > 145 ) = 44.811\%$