Please answer these questions with the information provided

1) A company audit showed that of 867 bills that were sent out, 565 were paid on time, 122 were paid up to 30 days late, 75 were paid between 31 and 90 days late, and 105 remained unpaid after 90 days. One bill is selected at random. a) What is the probability that the bill was paid on time? b) What is the probability that the bill was paid, but it was paid late? c) What is the probability that the bill was unpaid after 90 days? 2) A baseball pitcher threw 3848 pitches during part of a recent season. Of these, 1372 were thrown with no strikes on the batter, 961 were thrown with one strike, and 1515 were thrown with two strikes. Find the following: a) P(A baseball pitch is thrown with no strikes) = b) P(A baseball pitch thrown with fewer than two strikes): 3) In a survey 46,281 women were asked how many children they had. The results were as follows. Number of children 8 or more 7'22 0 12,574 1 7,493 2 11.282 3 2,124 4 3,??8 Numberofwomen 1,811 924 523 s ' s l 7 a) P(sampled woman has exactly 4 children}? b) P(Sampled woman has more than 3 children)? (3) Assume this is a simple random sample of U.S. women. Use the Empirical Method to estimate the probability that a woman has more than seven children. d) Using a cutoff of 0.05, is it unusual for a woman in the survey to have no children? (Hint: Find the probability the woman has no children.)