The batting average of a baseball player is the number of “hits” divided by the number of “at-bats.” Recently, a certain major league player’s at-bats and corresponding hits were recorded for 200 consecutive games. The consecutive games span more than one season. Since each game is different, the number of at-bats and hits both vary. Use this Frequency distribution to answer the following questions for the games where the player had exactly four at-bats.
| Number of Hits | Frequency |
| 0 | 10 |
| 1 | 29 |
| 2 | 26 |
| 3 | 4 |
| 4 | 3 |
A. Compute the mean number of hits.(X1 represents no. of hits and f1 represents the corresponding frequency). Explain what the numerical results mean. (This is the formula for the mean).
B. From the frequency distribution, construct the corresponding probability distribution. Explain why it is a probability distribution.
C. Using the frequency distribution, what is the player’s batting average for four at-bats? In part A, note that the numerator in the formula for the mean is the total number of hits. The total number of at-bats is the denominator of the formula for the mean multiplied by 4.
D. The Binomial Distribution is uniquely determined by n, the number of trials, and p, the probability of “success” on each trial. Using Excel, construct the Binomial Probability Distribution for four trials, n, and the probability of success, p, as the batting average in part 5. Here is an explanation of the BINOM.DIST function in Excel.
For example, In Excel
=BINOM.DIST(7,15,0.7, FALSE)
represents the probability of 7 successes out of 15 (n) trials. The 0.7 is the probability of success, p.
E. Using the formula for the mean of the binomial distribution, what is the mean number of successes in part D up above?