Question

The mean batting average in a certain baseball league is about 0.220. If batting averages are normally distributed, the standard deviation in the averages is 0.07, and there are 270 batters, what is the expected number of batters with an average of at least 0.500?

Answer 1

The mean batting average in a certain baseball league is about 0.220.

Batting averages are normally distributed with standard devaition of 0.07.

There are 270 batters. We have to find the expected number of batters, with an average of at least 0.500.

Here, batting avearge is the random variable under interest.

If X be the random variable denoting the batting average of a randomly selected player, then X follows normal distribution with mean 0.220, and standard deviation of 0.07.

So, Z = (X-0.220)/0.07 follows standard normal.

We find

=P(Z>(0.500-0.220)/0.07)

=P(Z>4)

Now , a standard normal variate lies within -3 and 3.

So, this probability is approximately 0.

So, the approximate number of players with batting average at least 0.500, is approximately 0.