7. Mensa is an organization that allows people to join only if their Stanford-Binet IQs are in the top 2% of the pop- ulation. Assume the population mean of Stanford-Binet IQs is 100, and the standard deviation is 15, and that the population is normally distributed. (a) What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa? (b) What is 99th percentile for the Stanford-Binet IQ scores? (c) What is the probability that a randomly selected per- sons Stanford-Binet IQ is between 85 and 115? (d) What is the probability that two randomly selected people both have Stanford-Binet IQs which qualify them for Mensa? 8. Assume that average cost of a particular medication is $60, with standard deviation $5, and that the cost is normally distributed.10. (a) Find the first quartile for the price of the medication. ind the thir uartile for the price of the medica- b) Find the third q ile f he pri f th di tion. () Find the lower bound (lower fence) for the boxplot- method of finding outliers for the price of the medi- cation. (d) Find the upper bound (upper fence) for the boxplot- method of finding outliers for the price of the medi- cation. (e) How many standard deviations away from the mean was the upper bound found in (d)? . The heights of men in a certain population follow a nor- mal distribution with mean 69.7 inches and standard de- viation 2.8 inches. (a) If 10 men are selected at random, what is the prob- ability their average height is above 72 inches? (b) If exactly one man is selected at random, what is the probability his average height is above 72 inches? (c) What is the 80" percentile for the average height of 10 men? (d) What is the probability the average height of 10 men is between 70 and 71 inches? The population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard devi- ation is 15 milligrams. Assume the variable is normally distributed. (a) Find the probability the cholesterol content for a sin- gle egg is between 210 and 220. (b) Find the probability the average cholesterol content for 25 eggs is between 210 and 220. () Find the third quartile for the average cholesterol content for 25 eggs. (d) If we are told the average for 25 eggs is less than 220 mg, what is the probability the average is less than 210 mg? 11. You must use properties of linear combinations of random variables to solve these problems. (a) Let X be a random variable where ux = 23, 0% = 6. Find the mean of Y, where Y =-24+4X (b) Let X be a random variable where px = 23, 0% = 6. Find the variance of Y, where Y =-2+4X (c) Let X be a random variable where ux = 0, 0% = 1/4. Find the mean of Y, where Y =-10-3X (d) Let X be a random variable where px = 0, 0% = 1/4. Find the variance of Y, where Y =-10-3X