Question

The weight of high school football players is normally distributed with a mean of 195 pounds and a standard deviation of 20 pounds.The probability of a player weighing more than 238 pounds is a.0.0334 b.0.0486 c.0.0158 d.0.9842

Answer 1

Answer:

c)

The probability of a player weighing more than 238

P( X > 238) = 0.0174

Step-by-step explanation:

Step(i):-

Given mean of the normally distribution = 195 pounds

Given standard deviation of  the normally distribution

                                                              =  20 pounds.

Let 'x' be the random variable of  the normally distribution

Let   X = 238

$Z = \frac{x-mean}{S.D} = \frac{238-195}{20} = 2.15$

Step(ii):-

The probability of a player weighing more than 238

P( X > 238) = P( Z> 2.15)

                  = 1 - P( Z < 2.15)

                 =  1 - ( 0.5 + A(2.15)

                =   1 - 0.5 - A(2.15)

               = 0.5 - 0.4821    ( from normal table)

               = 0.0174

The probability of a player weighing more than 238

P( X > 238) = 0.0174