1. The population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard devia tion is 18 milligrams. (Eggs are randomly selected.) (a) Find the probability the average cholesterol content for 36 eggs is between 210 and 220. (b) Find the third quartile for the average cholesterol content for 36 eggs. (c) If we are told the average for 36 eggs is less than 220 mg, what is the probability the average is less than 210 mg? 2. A fair coin is to be tossed 20 times. Find the probability that more than 15 of the tosses will fall heads, using the binomial distribution formula. using the normal approximation. z-xf'f-N a C79: vvv using the normal approximation with continuity correction. 3. Over 9 months, a random sample of 50 women were asked to record their average menstrual cycle length (in days). The sample average was 28.86 days, with a sample standard deviatiOn of 3.24 days. (a) Calculate the 90% condence interval for the true average menstrual cycle length. (b) Interpret the condence interval found in (a) in terms of the problem. (0) A researcher hypothesized that women's menstrual cycles are typically the same length as a lunar month 29.5 days. Does your interval from (a) support this hypothesis? (d) Are the assumptions for a condent interval met for this problem? 4. As part of a study of natural variation in blood chem- istry, serum potassium concentrations were measured in 81 randomly selected healthy women. The sample mean concentration was 5.36 mEq/l, and the sample standard deviation was 0.52 mEq/l. (a) Find the 95% condence interval for the true serum potassium concentrate in healthy women. (b) Interpret your condence interval found in (a) in terms of the problem. ((3) Does your interval support the claim that normal serum potassium concentrations are above 2.3? (d) If we were to build a 99% condence interval instead, would it widen or narrow