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- the following probability distribution represents the number of people living in a household (x), and the probability of occurrence (p(x). compute the expected value (mean), the variance, and standard deviation for the random variable. calculations for the mean.x 1 2 3 4 5p(x) .33 .29 .27 .07 .04A 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.Players would draw a card from a standard 52 card deck. Whatever card they drew determined what they won. If they draw a face card (Jack, King, Queen) then they win $5. If they draw an Ace, they win $15. For all other cards, they win nothing. A. Fill out the probability distribution table with the probabilities of each possible outcome for this game. Round decimals to four places. x $15 $5 $0 P(x) B. What is the expected value of the distribution above? (Round to the nearest cent, two decimal places.) C. If players were charged $2 per game, would they make and average profit on the games over time, or would they take an average loss over time? D. If players were charged $3 per game, would they make and average profit on the games over time, or would they take an average loss over time?
- A large number of MBA applicants are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What is the probability a randomly chosen applicant scores 600 or above in this test? a. 0.5401 b. 0.0401 c. 0.4599 d. 0.0852A 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…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 $12,485
- 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?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.)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.
- Anticipated consumer demand in a restaurant for free-range steaks next month can be modeled by a normal random variable with mean 1,200 pounds and standard deviation 100 pounds. a. What is the probability that demand will be between 1,100 and 1,300 pounds? Calculate in 4 decimal place. b. The probability is 0.10 that demand will be more than how many pounds?The score obtained on an emotional intelligence test is normally distributed,with an average score (μ) of 112 and a standard deviation (σ) of 8.5. What is the probability that a randomly selected person will:Q.6.3.1 Obtain a score between 111 and 116? Interpret your answer. Q.6.3.2 Obtain a score between 107 and 110? Interpret your answer.Given that Z is distributed as a standard normal random variable, what is Pr(Z > -0.04)? Round your answer to three decimal places, e.g. 0.251.