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

c)

The probability of a player weighing more than 238

P( X > 238) = 0.0174

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 = (x-mean)/(S.D) = (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