Question

The distribution of batting averages for players in the National League is approximately normal with a mean of 0.262 and a standard deviation of 0.039.

a. Find the probability​ (give 3 decimal​ places) that a player has a batting average of 0.300 or​ higher? Show all work and steps.

b. Only​ 25% of players have batting averages above what​ value? Give 3 decimal places. Show all work and steps.

Answer 1

let us consider x is the  batting averages for players in the National League which is normally distributed with

mean () = 0.262

and variance () = 0.039

a) P(x =   = P( = 0.1649

the probability​ that a player has a batting average of 0.300 or​ higher is 0.165

b ) from the z table value corresponding to 0.25 is .5987 so

x = = 0.262 + .5987 * 0.039

x = 0.285

Only​ 25% of players have batting averages above 0.285