Stat 2, Summer Session: Assignment 2 Instructions: YOU MUST SHOW ALL YOUR WORK TO RECEIVE FULL CREDIT. You will need a calculator and the normal table in the back of your textbook to do this assignment. If the value you need is in between two values in the normal table, use the one that is closest. (use the normal table ) 1. For each of the pictures below, use the normal table to calculate the shaded area underneath the normal curve. a) Answer: _________% b) Answer: _________% c) Answer: _________% Use the normal table to find the following percentiles of the normal curve. That is, find the value indicated by "?" in the pictures below. a) Answer: _________ standard units b) Answer: _________ standard units 3. A chain of coffee shops wants to standardize the amount of caffeine in an 8 oz. cup of the dark roast coffee they sell, so they hire a lab to measure it. The lab receives 50 samples and determines that they have an average of 140 mg of caffeine per cup, with a standard deviation of 12 mg. A histogram of the sampled values approximately follows the normal curve. a) We can infer that about 95% of the sampled cups had between _______ mg and _______ mg of caffeine. b) For each range of caffeine values, find the approximate percentage of cups in the range. Less than 130 mg: _______% Between 130 and 150 mg: _______% More than 160 mg: _______% c) What is the 90th percentile of the caffeine values? _______ mg 4. Dock jumping is a competitive sport for dogs, in which dogs jump off a dock into a body of water and the length of their jump is recorded. The Splash Dogs organization ranks dogs into divisions based on jump length, with dogs jumping between 20 and 23 feet considered "Pro" and over 23 feet considered "Extreme." Suppose a dock jumping competition is held, and the average jump length is 15 feet, the SD is 4.5 feet. A histogram of the jump lengths approximately follows the normal curve. a) Approximately what percent of the dogs in this competition would be considered "Pro?" Answer: _______% b) A dog jumped 13 feet, 2 inches. What was her approximate percentile rank? Answer: ________% c) Suppose that it is discovered that the jump measurements all started in the wrong place, so that all jumps were actually 1 inch longer than recorded. This is corrected. You do not need to redo (a) or (b), but answer: What is the new average jump length? ________________________ What is the new SD of the jump lengths? ________________________ Does the percentile rank of the dog from (b) change? Answer yes or no and explain your answer. 5. Heights among a league of professional male basketball players roughly follow the normal curve, with an average height of 6' 6", and an SD of 4". A new player joins the group and is described as being "taller than 99% of the rest of the players." How tall is this player? Round your answer to the nearest inch. Answer: ________________________ 6. In a large lecture course, the scores on the final exam followed the normal curve closely. The average score was 75 points and three-fourths of the class scored between 65 and 85 points. The SD of the scores was about _______ points. 7. Three data sets are collected, and the correlation coefficient is computed in each case. Fill in your best guess of each correlation coefficient in the blanks below, from the following possible values of r: -0.2 0 0.3 0.6 0.98 Each value can be used at most once; you will have two values left over. a) cumulative GPA after freshman year and cumulative GPA after sophomore year: r = ____________ b) cumulative GPA after freshman year and cumulative GPA after senior year: r = ____________ c) volume and weight of some pieces of aluminum, measured in a laboratory: r = ____________ 8. An ecologist is studying the flower Iris versicolor. She measures the width and length of 100 petals of this flower from a large collection of specimens and obtains the following data. Width: AVG = 1.2 cm, SD = 0.2 cm Length: AVG = 4.4 cm, SD = 0.5 cm r = 0.65 a) What is the 90th percentile of the widths, assuming that the histogram approximately follows the normal curve? b) Suppose the ecologist converts centimeters to inches, by dividing all the observations by 2.54. Put a check mark in front of everything that changes. ___ the average width ___ the SD of the lengths ___ the value of r ___ the 60th percentile of the widths ___ the percentile rank of petal with width 1.5 cm