An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 30% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)   (a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?   (b) If six reservations are made, what is the expected number of available places when the limousine departs?   places (c) Suppose the probability distribution of the number of reservations made is given in the accompanying table. Number of reservations     3 4 5 6 Probability     0.14         0.22         0.35         0.29    Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X. x 0 1 2 3 4 p(x)

Answer the following question accordingly:

16% of all Americans live in poverty. If 31 Americans are randomly selected, find the following probabilities. Round answers to 4 decimal places. a. Probability that exactly 4 of them live in poverty. b. Probability that at most 7 of them live in poverty. c. Probability that at least 5 of them live in poverty. d. Probability that between 1 and 6 (including 1 and 6) of them

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For question (a): 1) Write the probability statement 2) Draw and label a sketch of the distribution, indicating what it is that you are looking for, etc. 3) Show all work 4) Round to 4 decimal places, and circle your answer Then, answer question (b). Jim is the Director of quality Assurance for Oberweis. It is his job to make sure the machine that fills the pint bottles of milk for distribution in vending machines is working properly. The machine is regulated so that the amount of milk dispensed has a mean of 16 ounces and a standard deviation of 0.11 ounces. Jim selects 40 bottles of milk and carefully measures the contents. By his calculations, the sample mean of the bottles is 15.9 ounces, (a) What is the probability that a randomly selected sample of 40 milk bottles will contain an average of 15.9 ounces of milk or less? (b) What should Jim conclude about the machine? is it working properly?

A die numbered 1 through 6 is rolled twice. What is the probability of showing an odd number on the first roll and a number less than three on the second roll?