Answer:
0.33
Step-by-step explanation:
The proportion of pitchers have ERAs between 3 and 4=P(3<X<4)=?
[tex]P(3<X<4)=P(\frac{3-mean}{Standard deviation} <Z<\frac{4-mean}{Standard deviation} )[/tex]
[tex]P(3<X<4)=P(\frac{3-3.82}{1.14} <Z<\frac{4-3.82}{1.14} )[/tex]
[tex]P(3<X<4)=P(-0.72 <Z<0.16)[/tex]
[tex]P(3<X<4)=P(-0.72<Z<0)+P(0<Z<0.16)[/tex]
[tex]P(3<X<4)=0.2642+0.0636[/tex]
[tex]P(3<X<4)=0.3278[/tex]
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.
