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1.Under certain conditions it is possible that the sum of the probabilities of all the sample points in a sample space is less than one. ___ T/F 2.A compound event formed by use of the word and requires the use of the addition rule. ____ T/F 3.In any binomial probability experiment independent trials mean that the result of one trial does not affect the probability of success of any other trial in the experiment. ___ T/F 4.The sum of all probabilities in any discrete probability distribution is not always exactly one since some of the probabilities may be slightly larger than one. ___ T/F 5.If a random variable z is the standard normal score then the standard deviation of the distribution is 1. ____ T/F 6.Every binomial distribution may be approximated reasonably by an appropriate normal distribution ___ T/F 7.If P(A) = 0.45 P(B) = 0.35 and P(A and B) = 0.25 then P(A | B) is:A. 1.4 B. 1.8C. 0.714D.0.5568.Which of the following is a characteristic of a binomial probability experiment? A.Each trial has at least two possible outcomesB.P(success) = P(failure)C.The binomial random variable x is the count of the number of trials that occurD.The result of one trial does not affect the probability of success on any other trial9.If the random variable z is the standard normal score which of the following probabilities could easily be determined without referring to a table? A.P(z > 2.86)B.P(z C.P(z D.P(z> -0/5)10.In which of the following binomial distributions is the normal approximation appropriate? A.n = 50 p = 0.01B.n = 500 p = 0.001C.n = 100 p = 0.05D.n = 50 p = 0.02Part II. Short Answers & Computational Questions1. Find the following probabilities: a.Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.4 and P(A or B) = 0.9 find P(B). b.Events A and B are defined on a common sample space. If P(A) = 0.20 P(B) = 0.40 and P(A or B) = 0.56 find P(A and B) 2.Classify the following as discrete or continuous random variables a.the weight of bags of apples with 20 apples in a bagb.The number of times required for a modem to dial an internet provider before connecting c.A pair of dice is rolled and the sum to appear on the dice is recordedd.The time it takes to complete an exercise session.3.A small bag of Skittles candies has the following assortment: red (10) blue (2) orange (5) brown (21) green (0) and yellow (18). Construct the probability distribution for x. 4.Find the mean and standard deviation of the following probability distribution: x123P(x)0.30.50.25.In testing a new drug researchers found that 5% of all patients using it will have a mild side effect. A random sample of 11 patients using the drug is selected. Find the probability that: a)exactly two will have this mild side effectb)at least one will have this mild side effect. 6.A large shipment of TV sets is accepted upon delivery if an inspection of ten randomly selected TV sets yields no more than one defective TV. a)Find the probability that this shipment is accepted if 5% of the total shipment is defective.b)Find the probability that this shipment is not accepted if 10% of this shipment is defective7.X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities: a)P(x b)P(72.5 c)P(x >82.5) 8.Find the value of z such that 40% of the distribution lies between it and the mean. 9.Assume that the average annual salary for a worker in the United States is $27500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6250. Find the following: a)What percentage of Americans earn below $18000? b)What percentage of Americans earn above $40000?