Question

In 2004, professional baseball players in the National League had a mean batting average of 0.260 for the year with a standard deviation of 0.040.

(a) What percentage of batters had an average above 0.300?

(b) What percentage of batters had an average between 0.100 and 0.200?

(c) What percentage of batters had an average between 0.200 and 0.300? Use the normal error curve table to do your calculations

Explain briefly plz!!!!

Answer 1

Given,

The batting average of 2004, had a mean of 0.260 and standard deviation of 0.04.

We know that sample average tends to follow a normal distribution. Thus we have,

Let denote the cumulative distribution function of Normal(0,1) distribution

Part a

To calculate : Percentage of batters had an average above 0.300 i.e.

Thus we can say that 15.86 % of batters had an average above 0.3

Part b

To calculate: percentage of batters had an average between 0.100 and 0.200 ie.

Thus we can say that 0.67 % of batters had an average between 0.1 and 0.2

Part c

To calculate: percentage of batters had an average between 0.200 and 0.300 ie.

Thus we can say that 077.45 % of batters had an average between 0.2 and 0.3

Note : All Values of are obtained from Standard Normal Tables.