A baseball player is asked to swing at pitches in sets of fo

A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. The probability distribution for hitting a particular number of pitches is given below. Determine the standard deviation for this discrete probability distribution.

x

0

1

2

3

4

P (x)

0.02

0.07

0.22

0.27

0.42

Solution

Consider:

Thus,      
      

Var(x) = E(x^2) - E(x)^2 =    1.1  

s(x) = sqrt [Var(x)] =    1.048808848   [ANSWER]