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- The table gives the joint probability distribution of the number of sports an individual plays (X) and the number of times she may get injured while playing (1) X=3 0.15 0.06 0.15 0.02 Y=4 Y=3 Y=2 Y=1 X=1 0.12 0.05 0.10 0.15 The covariance between X and Y. xy.is (Round your answer to two decimal places. Enter a minus sign if your answer is negative.) The correlation between X and Y, con(X, Y), is (Round your answer to two decimal places. Enter a minus sign if your answer is negative) An increase in the number of sports an individual plays will tend to X=2 0.08 0.05 0.03 0.04 the number of times she may get injured while playingusing 'standard Normal Table ' , calculate the following probabilities. 1. Pr(z < -1.12) 2. Pr(z >2.32) 3.pr(1.22 < z >2.53) 4.pr(-3.22 < z < 0.22) 5.pr(-2.36 < z < -0.50)The number of major snowstorms (that shut down businesses) has a Poisson distribution with rate 0.4 per month Hom January through March. A restaurant buys an insurance policy to insure against losses. The policy pays nothing for the first major snowstorm that occurs in January through March, but pays $2,000 for every major snowstorm thereafter for that period up to $6.000. a) Find the probability there are 4 or more snow storms during the 3-month period. b) Find the expected amount paid by the policy during the 3-month period.
- A campus finance officer finds that, for all parking tickets issued, fines are paid for 78% of the tickets. The fine is $2. In the most recent week, 620 parking tickets have been issued.a. Find the mean and standard deviation of the number of these tickets for which the fines will be paid.b. Find the mean and standard deviation of the amount of money that will be obtained from the payment of these fines.A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation of 44 ounces. What is the probability of filling a cup between 21 and 31 ounces? Round your answer to four decimal places.A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 59.0 minutes. Find the probability that a given class period runs between 50.75 and 51.0 minutes. Find the probability of selecting a class that runs between 50.75 and 51.0 minutes. (Round to three decimal places as needed.)
- Question Two a) The table below shows the probability distribution of the discrete random variable X. 2 3 4 5 7 P(X=x) 2p 2p 3p i. Find the value of p from the table above. Calculate the probability that at X is at least 5. Calculate the mean of the distribution. ii. 111.The diameters of ball bearings are distributed normally. The mean diameter is 99 millimeters and the standard deviation is 5 millimeters. Find the probability that the diameter of a selected bearing is greater than 109 millimeters. Round your answer to four decimal places.The joint probability distribution of two random variables, Xand Y, is given in the table below. Y=-4 Y--3 Y--1 Y-2 X--4 0.06 0.12 0.17 0.18 X--1 0.00 0.03 0.00 0.21 X-0 0.02 0.01 0.20 0.00 From the information in the table, calculate each of the following probabilities. Round your answers to two decimal places. (If necessary, consult a list of formulas.) (a) Given that Y=-3, compute the probability that X=0. Given that X2 -1, compute the probability that (b) Y2-3.
- he local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. Find the probability that exactly 6 tickets are written on a randomly selected day from this populationAssume that the traffic to the web site of Smiley's People, Inc., which sells customized T-shirts, follows a normal distribution, with a mean of 4.48 million visitors per day and a standard deviation of 900,000 visitors per day. (a) What is the probability that the web site has fewer than 5 million visitors in a single day? If needed, round your answer to four decimal digits, (b) What is the probability that the web site has 3 million or more visitors in a single day? If needed, round your answer to four decimal digits. (e) What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your answer to four decimal digits. (d) Assume that 85% of the time, the Smiley's People web servers can handle the daily web traffic volume without purchasing additional server capacity. What is the amount of we traffic that will require Smiley's People to purchase additional server capacity? If needed, round your answer to two decimal digits.…Insurance: An insurance company sells a 1-year term life insurance policy to an 84-year-old man. The man pays a premium of $1600. If he dies within 1 year, the company will pay $33,000 to his beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 84-year-old man will be alive 1 year later is 0.9537, Let X be the profit made by the insurance company. do Part: 0/2 Part 1 of 2 (a) Find the probability distribution. The probability distribution is 1600 P (x)