Question

Normal Distribution problem: The mean batting average in a certain baseball league is about 0.280. Supposing that batting averages are normally distributed, that the standard deviation in the averages is 0.03, and that there are 290 batters, what is the expected number of batters with an average of at least 0.4?

Answer 1

If you normalize, you get z = (0.4-0.28)/0.03 = 4
Then you find probability P(z<4) from table. It is close to 1
Them you calculate 1 - P(z-4) because at least means
Batters, whose average is 0.4 or more.
Them you Multiply it by 290