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If the joint probability is given by: x + y f(x, y) = 30 for a = 0, 1,2, 3; y = 0, 1,2,
find P(X + Y = 4).
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- a) For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table. Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is (i) Is Silver car from Germany (ii) a black or white car manufactured in Korea. (iii) not manufactured in Japan. (iv) is a white car, given that it was manufactured in America. (v) Are the events 'Korea' and 'Black' Mutually Exclusive? Justify your response.According to the U.S. Bureau of the Census, about 75% of commuters in the United States drive to work alone. Suppose 150 U.S. commuters are randomly sampled. (a) What is the probability that fewer than 105 commuters drive to work alone?(b) What is the probability that between 116 and 126 (inclusive) commuters drive to work alone?(c) What is the probability that more than 96 commuters drive to work alone?A regional automobile dealership sent out fliers to perspective customers indicating that they had already won one of the three different prizes: automobile valued at $25,000, a $100 gas card, or a $5 Walmart shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership’s showroom. The fine print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,748, the chance of winning the gas card was 1 out of 31,748, and the chance of winning the shopping card was 31,746 out of 31,748.How many fliers the automobile dealership sent out? Please explain. Using your answer to above and the probabilities listed on the flyer, what is the expected value ofthe price won by a prospective customer receiving a flyer? Demonstrate all necessary steps. Using your answer to the first question and the probabilities listed on the flyer what is the standarddeviation of the value of the price one by the…
- ( e )Given that the population has a normal distribution with average equal to 60 and standard deviation of 40. Find the probability that: (i)P(x>/=120)(ii)P(10 </=X</=140)What is the probability of P(Z< -1.07)a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet (i) Define the random variable for this situation and list its values (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii)State the conditions that influence your choice of distribution. (iv)Calculate the probability that at most 2 of the roses were Eden Roses. b) The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute. (i) Define the random variable in this situation and list its values. (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii)Compute the probability that 5 calls will arrive per minute. (iv)Compute the probability that 3 or more calls will arrive in a 3-minute interval?
- Suppose N = 15 and r = 4. What is the probability of x = 3 for n = 10 (to 4 decimals)?Find the probabilities for each, using the standard normal distributionFor a group of 300 cars the numbers, classified by color and country of manufacture, are shown in the Black Silver White Total Korea 33 34 35 102 Japan 23 9 24 56 America 16 25 34 75 Germany 19 16 32 67 Total 91 84 125 300 One car is selected at random from this group. Find the probability that the selected car is A black or white car manufactured in Korea.
- For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is a black or white car manufactured in Korea.An equipment proposal from two vendors A and B have been received from a local company. The quality of these equipment have been varying and consequently the cost of manufacturing the product using these two different equipment has also varied. The varying costs based on the probabilities of defects are given in table below.Determine the better vendor.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.