(all problems in EXCEL FILE with the formulas on and provide the excel link )

Problem 1 The random variable x is known to be uniformly distributed between 1.0 and 1.5. a. Show the graph of the probability density function. b. Compute ( =1.25). c. Compute (1.0 1.25). d. Compute (1.20< <1.5). Problem 2 Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $15,000. a. Suppose you bid $12,000. What is the probability that your bid will be accepted? b. Suppose you bid $14,000. What is the probability that your bid will be accepted? c. What amount should you bid to maximize the probability that you get the property? d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not? Problem 3 Given that z is a standard normal random variable, compute the following probabilities. a. (1.0) b. (1) c. (1.5) d. (2.5) e. (3<0) Problem 4 In an article about the cost of health care, Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $328 (Money, January 2009). Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $92. Answer the following questions about the cost of a hospital emergency room visit for this medical service. a. What is the probability that the cost will be more than $500? b. What is the probability that the cost will be less than $250? c. What is the probability that the cost will be between $300 and $400? d. If the cost to a patient is in the lower 8% of charges for this medical service, what was the cost of this patient's emergency room visit?