One professional golfer plays best on short-distance holes. Experience has shown that the numbers x of shots required for 3-, 4-, and 5-par holes have the probability distributions shown in the table below. Par-3 Holes Par-4 Holes Par-5 Holes X p(x) X p(x) X p(x) 0.12 3 0.14 4 0.02 3 0.80 4 0.80 5 0.80 4 0.06 5 0.04 6 0.14 5 0.02 6 0.02 7 0.04 What is the golfer's expected score on these holes? (a) a par-3 hole (b) a par-4 hole (c) a par-5 holeThe maximum patent life for a new drug is, in most cases, 20 years. Subtracting the length of time required by Health Canada for testing and approval of the drug provides the actual patent life of the drug-that is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here. Years, x 3 4 5 6 7 8 9 10 11 12 13 p(x) 0.01 0.05 0.07 0.10 0.14 0.21 0.19 0.12 0.07 0.03 0.01 (a) Find the expected number of years of patent life for a new drug. (Enter your answer to two decimal places.) yr (b) Find the standard deviation of X. (Round your answer to four decimal places.) yr (c) Find the probability that X falls into the interval u + 20. (Enter your answer to two decimal places.)Let x equal the number observed on the throw of a single balanced die. (a) Find and graph the probability distribution for x. p(X) p(x) 0.3 P(x) P(x) 0.3- 0.2- 0.2 0.1 0.2 WebAssign Plot 0.1 0.1 0.1 1 2 3 X 4 5 6 1 2 3 X 4 5 6 1 2 3 x O 1 4 3 X 5 2 6 4 5 6 X (b) What is the average or expected value of x? (c) What is the standard deviation of x? (Round your answer to two decimal places.) (d) Locate the interval u + 20 on the x-axis of the graph in part (a). What proportion of all the measurements would fall into this range?If an experiment is conducted, one and only one of three mutually exclusive events 51* 52, and 53 can occur, with these probabilities. 0:31) = 0.4 p.132) = 0.5 #1533. = 0.1 The probabilities of a fourth eventA occurring, given that event 51, 52, or 53 occurs, are the following. P(A|31] = 0.4 P[A|32} = 0.2 P(A|53] = 0.1 If event A is observed, find P(51|A), P[52|A], and P[53|A]. (Round your answers to four decimal places.) 05M: = x 052m: = E .w = S 24. [0/1 Points] DETAILS PREVIOUS ANSWERS MENDSTATC4 4.E.076. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A worker-operated machine produces a defective item with probability 0.05 if the worker follows the machine's operating instructions exactly, and with probability 0.07 if he does not. If the worker follows the instructions 90% of the time, what proportion of all items produced by the machine will be defective? 5.2% X 25. [-/1 Points] DETAILS MENDSTATC4 4.E.079. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Many public schools are implementing a "no pass, no play" rule for athletes. Under this system, a student who fails a course is disqualified from participating in extracurricular activities during the next grading period. Suppose the probability that an athlete who has not previously been disqualified will be disqualified is 0.15 and the probability that an athlete who has been disqualified will be disqualified again in the next time period is 0.5. If 40% of the athletes have been disqualified before, what is the unconditional probability that an athlete will be disqualified during the next grading period? (Enter your answer to three decimal places.)A sample space S consists of five simple events with these probabilities. P(E, ) = P(E2) = 0.15 P(E3) = 0.55 P( EA ) = 2P(E5) (a) Find the probabilities for simple events E and Es. P(E) = .10 P(E,) = .05 (b) Find the probabilities for these two events. A = {E , E3, E4} B = {E,, Ez} P(A) = .80 P(B) = 1.70 (c) List the simple events that are either in event A or event B or both. (If there are no simple events, enter NONE.) E1, E2, E3, E4 X (d) List the simple events that are in both event A and event B. (If there are no simple events, enter NONE.) E3 Xprobability as a fraction.) 64 X