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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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- The closing price of Martin's Sporting Goods Inc. common stock is uniformly distributed between $25 and $36 per share. What is the probability that the stock price will be more than $32?The proportion of vehicles which drive above the speed limit on a freeway is 85%. Suppose 100 vehicles are randomly clocked. 20 If each speeding vehicle is issued a $185 speeding ticket, the expected value of the ticket amount is $________. a $15,725 b $14,560 c $13,480 d $12,485For 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.
- A company that manufactures and sells T-shirts for sporting events, is providing shirts for an upcoming tournament. Each shirt will cost $7 to produce and will be sold for $13. Any unsold shirts at the end of the tournament can be sold for $5 apiece in the near future. The company assumes the demand for the shirts will be 1,500,3,000,4,500, or 6,000. The company also estimates that the probabilities of each of these sales levels occurring will be 20%, 25%,25%, and 30%, respectively. Determine the expected monetary value of the project if the company chooses to print 4,500 shirts for the tournament. The expected monetary value is---- (Type a whole number.)If the heights of women are normally distributed with a mean of 64 inches and a standard deviation of 1 inch, the probability of randomly selecting a woman smaller than 62.5 inches isGiven a binomial distribution, n = 6 and π = .25. Determine the probability given x = 2 using the binomial formula.
- Applied Machines produces large test equipment for integrated circuits. The machines are made to order, so the production rate varies from month to month. Before shipping, each machine is subject to extensive testing. Based on the tests the machine is either passed or sent back for rework. During the past 20 months the firm has had to rework the following numbers of machines: (given) Consider the example of Applied Machines presented above. Based on the estimate of the probability that a machine is sent back for rework computed from the 20 months of data, determine the following:a. If the company produces 35 machines in one particular month, how many, on average, require rework?b. Out of 100 machines produced, what is the probability that more than 20 percent of them require rework? (Use the normal approximation to the binomial for your calculations).For 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.A random variable has a triangular probability density function with a = 50, b = 375, and m = 250. What is the probability that the random variable will assume a value between 60 and 250? If required, round your answer to four decimal places.
- Converting to the standard normal random variable z, the probability statement P(x ≥ 43.5) is now P(z ≥ 3.90). Recall that the normal probability table gives area under the curve to the left of a given z value. Since we want the area to the right of z = 3.90 and the area under the entire curve is 1, the area to the left of z = 3.90 can be subtracted from 1. Use the table to find the probability that a student who has done their homework and attended lectures will obtain a grade of A on this test, P(z ≥ 3.90), rounding the result to four decimal places. P(z ≥ 3.90) = 1 − P(z ≤ 3.90) = 1 − =A quality control expert at LIFE Batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 77 minutes with a mean life of 551 minutes. If the claim is true, in a sample of 135 batteries, what is the probability that the mean battery life would be greater than 545.6 minutes? Round your answer to four decimal places.A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the two machines were purchased at the same time. The estimated probability of low demand is .30, and the estimated probability of high demand is .70. The net present value associated with the purchase of two machines initially is 950,000 if demand is low and 1,300,000 if demand is high. The net present value for one machine and low demand is 900,000. If demand is high, there are three options. One option is to do nothing, which would have a net present value of 1,000,000. A second option is to subcontract; that would have a net present value of 1,400,000. The third option is to…