1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.
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- 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?The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?Help me with 11. Please
- 7. The amount spent by a customer on a Summer Cruise has a normal distribution with a mean of $95.60 and a standard deviation of $5. a) Calculate the probability that a randomly selected customer spends less than $95. b) The probability that customers spend more than x dollars is 0.2810. Find the value of r.The injured football player Bad news everyone! There is 1 second left in the game, and Tom Brady has injured himself. The matrices below depict the relative probabilities of winning givenan offensive and a defensive play call. (The row player is the New England Patriots and the column player is the opponent.) How much has the all star's home team probability of winning decreased due to the injury? Pass uny Patriots D Pass .4, .6 D Run .9,.1 .8,.2 .5,.5 Pass Run Opponent D Pass D Run .06, .94 .32, .68 .8,.2 .5,.5a. A company produces lightbulbs whose life follows a normal distribution, with mean 1200 hours and standard deviation 250 hours. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1300 hours? (answer in three decimal places)
- How would you find the probabilities for this question? (see attachment)A construction company needs to move lumber onto the roof of a building. If the lumber falls and hits someone it will cause $1,200,000 in damage. Assume that company must choose between the following levels of precaution: Spend $500 and the probability of an accident is .05 Spend $5,000 and the probability of an accident is .01 Spend $8,000 and the probability of an accident is .008 Spend $10,000 and the probability of an accident is .003 If the construction company is strictly liable for the costs of the accident, how much would they spend on precaution? A. $500 B. $5,000 C. $8,000 D. $10,0001. Imagine a person who wants to find a job within two months. Define X corresponding to the outcome, such that X = 1 if the person finds a job and X = 0 otherwise. (a) Explain why X can be viewed as a random variable. What is the support of X? (b) Suppose the probability of finding a job is 0.75. What is the probability distribution of X? Be specific.
- 3. A salesman who frequently drives from Muscat to Sohar finds that his driving time is a random variable having roughly a normal distribution with mean 4.3 hours and standard deviation 0.2 hour. Find the probabilities that such a trip will take a. more than 4.0 hours, b. less than 5.0 hours. C. Between 3.5 and 5.5 hoursDN4 Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Probability (Investment B) Payoff $300 $250 $200 Probability (Investment A) 0.10 0.80 0.10 0.30 0.40 0.30 Nahoko has the utility function U= 51, where I denotes the payoff. Which investment should she choose?Suppose that the distribution of Uber rides around the quoted arrival time is normally distributed. Themean waiting time (relative to the quoted time) is 0, with a standard deviation of 3 minutes.a. Using the empirical rule, what percentage of rides arrive within 3 minutes of the mean (3 minutesbefore to 3 minutes after)?b. Graphically depict the area that would need to be calculated to determine the probability ofwaiting more than 4 minutes for a ride. Explain your graph.