1. The Villanova Wildcats won the 2018 men's college basketball national championship. Their distribution of points scored had a mean of 86.6 points, a standard deviation of 10.8 points and follows a normal distribution. a) Calculate AND interpret the z-score for the game where they scored 121 points. Show work. b) Calculate AND interpret the z-score for the game where they scored 61 points. Show work. c) In one game, their z-score was 0.59. How many d) Sketch a curve and label the mean + 3 points did they score in that game? Show work. standard deviations from the mean. (Include the corresponding percentages.) e) In what interval would you expect to find f) What percent of the data would you the middle 99.7% of the data? expect to find between 75.8 and 108.2 pts? g) What percent of the time did the Wildcats h) What percent of the time did the Wildcats score less than 70 points? Show work. score at least 100 points? Show work. i) How many points do the Wildcats need to score to be in the top 15%? Show work.2) In the 2016 Olympics, U.S. swimmer Katie Ledecky won 4 gold medals and set two world records: a time of 236.46 seconds in the 400-meter freestyle and a time of 484.75 seconds in the 800-meter freestyle. In the 400-meter freestyle, the mean time for the 8 finalists was 242.98 seconds with a standard deviation of 1.79 seconds. While in the 800-meter freestyle, the mean time for the 8 finalists was 501.09 seconds with a standard deviation of 3.95 seconds. Which of these record- setting performances was better? Show all work and explain your answer. 3) During practice for the Indy 500 in 2017, driver Marco Andretti's distribution of lap speed has a mean of 223.7 mph. Assume that the distribution was roughly normal with a standard deviation of 4.2 mph. Sketch a normal curve and label the mean + 3 standard deviations (along with percentages). 4) Alex is applying for college and has taken both the SAT and the ACT. She only wants to submit her best score, but doesn't know which one to submit. She scored 1280 on the SAT and 27 on the ACT. In 2017, the distribution of SAT scores had a mean of 1060 and a standard deviation of 195 while the distribution of ACT scores had a mean of 20.8 and a standard deviation of 5.6. Which score should Alex submit? Show all work and explain your answer. 5) Michael is at the 80th percentile of grades in his Geometry class. Explain what it means to be at the 80th percentile in this scenario. 6) Name 3 other 'waysames' to describe the shape of the Normal distribution.7) The distribution of the weight of an oreo cookie is roughly normal with a mean of 11.39 grams and a standard deviation of 0.08 gram. a) What percentage of oreo cookies would you expect to weigh more than 1 1.51 grams? Show work. b) What percentage of oreo cookies would you expect to weigh at most 1 1.25 grams? Show work. c) Would you be surprised if you were given an oreo cookie that weighed 1 1.60 grams? Show work and explain your answer. d) Estimate the weight of an oreo cookie at the 40 percentile. Show work. 8) A study investigated about 3,000 meals ordered from Chipotle restaurants using the online site Grubhub. Researchers calculated the sodium content (in milligrams) for each order based on Chipotle's published nutrition information. The distribution of sodium content is roughly normal with a mean of 2,000 mg and a standard deviation of 500 mg. a) The next meal you order from Chipotle has a sodium content of 2,640 mg. Calculate the z-score associated with this value AND interpret this z-score in context. b) What percentage of meals from Chipotle would you expect to have a sodium content between 1,850 and 2,475 mg? Show work.#3 cont. :3}: Estimate the value of the 95* percenttle of sodium content in lChipotle meals. Show work. '9'] A bottling company fills bottles labeled '2 ters' with delicious diet cola. Of course, there is some variation from the target volume. In fact, the distribution of volume is roughly.r normal with a mean of 2.04 liters and a standard deviation of 0.03 liter. at About what percentage of bottles are underlled [less than 2 liters]? Show work. bt About what percentage of bottles have a volume greater than 2.1K} liters? Show work. :3}: About what percentage of bottles are within 0.05 liter of the target volume [i.e. between 1.95 and 2.05 liters] ? Show work. d] Estimate the value at the .75\" percentile for this distribution. Show work. TU] L'la'hat percentile corresponds to the lower 35% at a data set? ll] L'la'hat percentile corresponds to the top 8% of a data set