Question

Suppose a baseball player had 229 hits in a season. In the given probability distribution, the random variable x represents the number of hits the player obtained in a game. Round one decimal place. show work.

x...........0......1......2......3......4......5

P(x)..0.1712...0.4886....0.2389....0.0706.....0.0256.......0.0051

a.) Compute and interpret the mean of the random variable x

?x =

Which of the following interpretations is correct?

1.) As the number of trials n decreases, the mean of the observations will approach the mean of the random variable.

2.) As the number of trials n increases, the mean of the observations will approach the mean of the random variable.

3.) The observed value of the random variable will almost always be less than the mean of the random variable.

4.) The observed value of the random variable will almost always be equal to the mean of the random variable.

b.) Compute the standard deviation of the random variable x.

?x =

Answer 1

a) summation of p(x)/n ie. (0.1712+...+0.0051)/6=0.16675

b)1

c).var=summation (x-mean) squared /n ie (0.1712-0.16675)squared +...+(0.0051-0.16675)squared/n=0.027351948

SD =square root of variance =0.16538

Explanation: