1. Let X be normally distributed with mean = 2.5 and standard deviation =2 a. Find P(X > 7.6) (round z value 2 decimal places and final answer 4 decimal places) b. Find P(7.4 < X < 10.6) (round z value 2 decimal places and final answer 4 decimal places) c. Find x such that P(X > x) = 0.025 (round z value and final answer 2 decimal places) d. Find x such that P(x < X < 2.5) = 0.4943 (round z value and final answer 2 decimal places) 2. Let x be normally distributed with mean = 120 and standard deviation = 20 a. Find P(X < 86) (round z value 2 decimal places and final answer 4 decimal places) b. Find P(80 < X < 100) (round z value 2 decimal places and final answer 4 decimal places) c. Find x such that P(X < x) = 0.40 (round z value and final answer 2 decimal places) d. Find x such that P( X > x) = 0.90 (round z value and final answer 2 decimal places) 3. Let x be normally distributed with mean = 2,500 and standard deviation = 800 a. Find x such that P(X < x) = 0.9382 (round z value to 2 decimal places and final answer to nearest whole number) b. Find x such that P(X > x) = 0.025 (round z value to 2 decimal places and final answer to nearest whole number) c. Find x such that P(2,500 < X < x) = 0.1217 (round z value to 2 decimal places and final answer to nearest whole number) d. Find x such that P(X < x) = 0.4840 (round z value to 2 decimal places and final answer to nearest whole number) 4. The time required to assemble an electronic component is normally distributed with a mean and standard deviation of 16 minutes and 4 minutes, respectively. a. Find the probability that a randomly picked assembly takes between 10 to 20 minutes. Probability = (round z value 2 decimal places and final answer 4 decimal places) b. It is unusual for the assembly line to be above 24 minutes or below 6 minutes. What proportion of assembly times fall in these unusual categories? Proportion of assembly times = (round z value 2 decimal places and final answer 4 decimal places) 5. You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 8% with a standard deviation of 14%. The relatively less risky fund promises an expected return and standard deviation of 4% and 5%, respectively. Assume that the returns are approximately normally distributed. a. Calculate the probability of earning a negative return for each fund. (round z value 2 decimal places and final answer 4 decimal places) Riskier fund = Less risky fund = b. Which mutual fund would you pick if your objective is to minimize the probability of earning a negative return? c. Calculate the probability of earning a return above 8% for each fund. (round z value 2 decimal places and final answer 4 decimal places) Riskier fund = Less risky fund = d. Which mutual fund will you pick if your plan is to maximize the probability of earning a return above 8%? 6. A packaging system fills boxes to an average weight of 18 ounces with a standard deviation of 0.2 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd, and 3rd quartiles of the box weight. (round z value and final answer to 2 decimal places) a. 1st Quartile = b. 2nd Quartile = c. 3rd Quartile =