1. Find the mean μ and standard deviation σ of a random variable x with the following probability distributionx0123P(x)0.30.30.30.1(a) μ = 1.5 σ = .96(b) μ = 1.2 σ = .96(c) μ = 1.5 σ = .98(d) μ = 1.2 σ = .98(e) μ = 1.5 σ = 2.42. According to a survey reported in the Business Week, 30% of adults in the U.S. said that the cell phone is the invention that they hate most but cannot live without. If a random sample of 6 adults in the U.S. is selected, find the probability that at least 3 in the sample hold this opinion.(a) .1852(b) .0595(c) .0102(d) .0007(e) .2556To set a schedule for a new bus route the transit authority repeatedly times the trip between twopoints; the time x in minutes is found to have the probability distribution shown.25.043. The probability that a randomly selected trip will take at least 24 minutes is about:(e) .864. If the trip is made over and over, the average time it takes in minutes is about:(e) 23.05. According to the U. S. Center for Health Statistics the probability that a randomly selected twenty year old will live to age 65 is 80%. A club has twenty members aged twenty. What are the chances that at least one fourth of them will die before their 65th birthdays?59% (b) 63% (c) 20% (d) 80% (e) 37%6. Only 10% of American adults can name the capital of the Czech Republic. On a television game show the three randomly selected contestants are given the question “What is the capital of the Czech Republic?” The probability that none of them will know the answer is about:(e) 52%Questions 7 and 8. The following table gives the possible net gains (in dollars) of agambling game and the corresponding probabilities50.017. If you play this game once, what is the probability that your net gain is $20 or more?(e) .038. Find the expected value of this game (that is, μ= E(x)).(e) -$0.4Problems 9 and 10 pertain to the following situation:The number x of errors on a randomly selected page of a textbook has the following probabilitydistribution. No page has more than four errors.4.90 .06 .03 .005 .0059. The probability that a randomly selected page contains at least one error is about(a) 0.04 (b) 0.90 (c) 0.06 (d) 0.10 (e) .9610. The average number of errors per page is about(a) 10 (b) .155 (c) .20 (d) 1.55 (e) .0612. A basketball player makes 70% of his free throws. If he is awarded 20 free throws, then the probability that he will make between 12 and 16 of them (including 12 and 16) is about(a) .14 (b) .78 (c) .70 (d) .53 (e) .2213. A man buys twenty $1 lottery tickets per week. The chance of buying a winning ticket is 5%. The average number of winning tickets that he buys per week is8 (b) 0 (c) 5 (d) 1 (e) 15Problems 14 and 15 pertain to the following situation:Every day for six months a commuter records the number x of minutes his train ride to work takes, and obtains the probability distribution:29.0814. The probability that a randomly selected train ride will last at least 25 minutes is about:(e) .4115. The average length of the daily train ride in minutes is about:(e) 26.116. One in five $1 lottery tickets wins the buyer some kind of payoff. If a person buys five tickets, the probability that none will be a winning ticket is about:(e) .52For questions 17 and 18: A coin is tossed 5 times and x is the number of times a tailshows up. The following table gives the probability distribution of x.51/3217. Find P(x ≥ 3.4).(e) 26/3218. Find μ = E(x).(e) 3.019. Six percent (6%) of all shoppers make an impulse purchase at the check-out counter in a grocery store. If a store has 650 customers each day, what is the average number of impulse purchases made per day at the check-out counter?(e) 3920. Twelve percent (12%) of the population write with their left hands. Six students enter a classroom that has one left-handed desk free. What is the probability that exactly one of the six students writes with his left hand?(e) .88