According to the Daily Racing Form, the probability is about 0.67 that the favorite in a horse race will finish in the money (first, second, or third place). In the next five races, what is the probability that the favorite finishes in the money
a. Exactly twice?
b. Exactly four times?
c. At least four times?
d. between two and four times, inclusive?
e. Determine the probability distribution of the random variable X, the number of times the favorite finishes in the money in the next five races.
f. Identify the probability distribution of X as right skewed, symmetric, or left skewed without consulting its probability distribution or drawing its probability histogram.
g. Draw a probability histogram for X.
h. Use your answer from part (e) and Definitions 5.9 and 5.10 on pages 217 and 219, respectively, to obtain the mean and standard deviation of the random variable X.
i. Use Formula 5.5 on page 230 to obtain the mean and standard deviation of the random variable X.
j. Interpret your answer for the mean in words.