uniformly a. If she leaves the house on the market for another month, what is the mathematical the expression for the probability density function of the sales price? b. If she leaves it on the market for another month, what is the probability that she will get at least $215,000 for the house? c. If she leaves it on the market for another month, what is the probability that she will get less than $210,000? d. Should the executive leave the house on the market for another month? Why or why not? NCAA Scholarships. The NCAA estimates that the yearly value of a full athletic scholarship at in-state public universities is $19,000 (The Wall Street Journal). Assume the scholarship value is normally distributed with a standard deviation of $2,100. a. For the 10% of athletic scholarships of least value, how much are they worth? b. What percentage of athletic scholarships are valued at $22,000 or more? c. For the 3% of athletic scholarships that are most valuable, how much are they worth? . Production Defects. Motorola used the normal distribution to determine the probab- ility of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1,000-unit production run in the following situations. a. The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. b. Through process design improvements, the process standard deviation can be re- duced to .05. Assume the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. c. What is the advantage of reducing process variation, thereby causing process con- trol limits to be at a greater number of standard deviations from the mean? Bringing Items to a Pawnshop. One indicator of the level of economic hardship in a community is the number of people who bring items to a pawnbroker. Assume the number of people bringing items to the pawnshop per day is normally distributed with a mean of 658. a. Suppose you learn that on 3% of the days, 610 or fewer people brought items to the pawnshop. What is the standard deviation of the number of people bringing items to the pawnshop per day? 000.202 b. On any given day, what is the probability that between 600 and 700 people bring items to the pawnshop?