Algebra II Unit 9 Day 2 Homework Name: ______________________ Date: ______________ Per: ____ 1. You score 680 on the mathematics portion of the SAT. The math scores on the SAT are normally distributed with a mean of 518 and a standard deviation of 114. Your friend scores 27 on the ACT mathematics test. The ACT math scores are normally distributed with mean 20.7 and standard deviation 5.0. Find each z-score. Who did comparatively better on their test, you or your friend? Why? 2. Determine the percentile of each Z-score: a) Z is less than 1.25 b) Between Z = -1.95 and Z = 1.75 c) Z is less than -2.45 d) Z is greater than 0.95 3. A vending machine is designed to disperse a mean of 7.8 oz of soda into an 8 oz cup. The standard deviation of the amount dispensed is 0.15 oz. Assuming that the amount of soda dispensed is normally distributed….. a) What is the probability that a randomly selected cup of soda has an amount less than 8 oz? b) What is the probability that a randomly selected cup of soda has greater than 7.9 oz? 4. The average American male is 69.3 inches tall with a standard deviation of 2.8 inches. Your father is 5’11”. a) What percent of the male U.S. population is shorter than your father? b) What percent of the male U.S. population is taller than your father? c) What percentage of males are between 63.7” and 74.9”? d) If there are 151,781,326 males in the United States, how many are between 65” and 70”? 5. The average American female is 5’4” with a standard deviation of 4”. a) What percent of women are between 5’ and 5’8’’? b) What percent of women are taller than 6’? c) If there are 156,964,212 females in the United States, how many are taller than 6’? 6. Based on the data in #4 or #5, what is YOUR height percentile?