Question

The ERA (earned run average) of starting pitchers is normally distributed with a mean of 3.82 and a standard deviation of 1.14. What proportion of pitchers have ERAs between 3 and 4?Group of answer choices0.720.560.240.33

Answer 1

0.33

Explanation:

The proportion of pitchers have ERAs between 3 and 4=P(3<X<4)=?

`P(3<X<4)=P((3-mean)/(Standard deviation) <Z<(4-mean)/(Standard deviation) )`

`P(3<X<4)=P((3-3.82)/(1.14) <Z<(4-3.82)/(1.14) )`

`P(3<X<4)=P(-0.72 <Z<0.16)`

`P(3<X<4)=P(-0.72<Z<0)+P(0<Z<0.16)`

`P(3<X<4)=0.2642+0.0636`

`P(3<X<4)=0.3278`

Rounding to 2 decimal places

P(3<X<4)=0.33.

Thus, the proportion of pitchers have ERAs between 3 and 4 is 0.33.