In the game of baseball, every time a player bats, he is either successful (gets on base) or he fails (doesn't get on base). (This is all you need to know about baseball for this problem!) His on-base percentage, usually expressed as a decimal, is the percentage of times he is successful. Let's consider a player who is theoretically a 0.375 on-base batter. Specifically, assume that each time he bats, he is successful with probability 0.375 and unsuccessful with probability 0.625. Also, assume that he bats 600 times in a season. What can you say about his on-base percentage, (# of successes)/600, for the season?
(Hint: Each on-base percentage is equivalent to a number of successes. For example, 0.380 is equivalent to 228 successes because 0.380*600 = 228.)
a. What is the probability that his on-base percentage will be less than 0.360?
b. What is the probability that his on-base percentage will be greater than 0.370?
c. What is the probability that his on-base percentage will be less than or equal to 0.400?