Question Help * Suppose a baseball player had 224 hits in a season In the given

Question

Question Help * Suppose a baseball player had 224 hits in a season In the given probability distribution, the random variable X represents the number of hits the player obtained in a game. P(x) 0.0902 0.4969 0.2897 0.0587 0,0272 (a) Compute and interpret the mean of the random variable X |0.0373 :D hits Round to one decimal place as needed.) Which of the following interpretation of the mean is correct? O A. As the number of experiments decreases, the mean of the observations will approach the mean of the random vanable O B. The observed value of an experiment will be equal to the mean of the random variable in most experiments. ° C. The observed value of an experiment will be less than the mean of the random variable in most experiments. O D. As the number of experiments increases, the mean of the observations will approach the mean of the random variable (b) Compute the standard deviation of the random variable X o,hits Round to one decimal place as needed) Click to select your answer(s)

Explanation / Answer

(a) Here,

x = 0 * 0.0902 + 1 * 0.4969 + 2 * 0.2897 + 3 * 0.0587 + 4 * 0.0272 + 5 * 0.0373 = 1.5477 or 1.5

Here the option D is correct for mean's interpreatation. NUmber of experiments increase will promote more mean of observation approach the mean.

(b) Var(X) = (0 -1.5477)2 * 0.0902 + (1 - 1.5477)2 * 0.4969 + (2 - 1.5477)2 * 0.2897 + (3 -1.5477)2* 0.0587 + (4 -1.5477)2 * 0.0272 + (5 -1.5477) 2 * 0.0373

= 1.156325

Standard ddeviation (X) = x = sqrt(1.156325) = 1.075325 or 1.1

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