Transcript Stat 226
Review Session STAT 226 POPULATION, PARAMETER, STATISTIC, SAMPLE Which goes with which? POPULATION, PARAMETER, STATISTIC, SAMPLE You are looking at the average age of all American alligators, you select 15 alligators off the coast of Florida and track them to see how old they become. The average of these 15 live to be 12. The true average age alligators live to is 16. POPULATION, PARAMETER, STATISTIC, SAMPLE Your dog can jump 2.5 feet. This leads you to believe your dog can jump farther than any other dog. However, the American record book has a dog that can jump 6.48 feet. POPULATION, PARAMETER, STATISTIC, SAMPLE The Iowa state football team has an average height of 6’2”. The NCAA average height for football players is 6’. You then conclude the ISU team is pretty tall. POPULATION, PARAMETER, STATISTIC, SAMPLE Oak trees live to be an average age of 263 years. The oak trees in America have been known to live an average of only 123 years. CATEGORICAL OR QUANTITATIVE Categorical : Quantitative: CATEGORICAL OR QUANTITATIVE Top 10 websites Number of roll – over car accidents based on car brand The baggage fees for different airlines collected each year Price of cars people purchased in 2008 Regional rain fall sales for 4 types of smart phones Height of 200 random people in Iowa Net Income Wine exports of the top 5 wine-exporting countries CATEGORICAL OR QUANTITATIVE Histogram Bar Graph Pie Chart Box Plot Pareto Chart CREATE A VISUAL The following table presents the sales of cars in the US broken down by manufacturer Manufacturer Car Sales Chrysler 107,172 Ford 166,441 General Motors 180,402 Honda 83,925 Nissan 85,182 Toyota 137,960 10 9 8 4 2 8 9 5 8 6 7 8 3 a) b) c) d) e) What is the sample size Find the median Find the IQR Find the mean The standard deviation in 1.38, what is the variance? NUMBER SUMMARIES When is the 5 number summary used over the mean and standard deviation? Car prices b) What is an advantage to having them side by side? Honda a) What is this graphic called? c) Give the 5-number summary for Honda Price (in 1000s) 62 d) What is the shape of the distribution of Nissan? Nissan 83 64 43 38 35 25 24 23 16 e) For which of the two distributions do you expect the corresponding mean to be closer to the median? f) Compare and contrast both distributions regarding their overall shape, center, spread and For the center and spread do not simply state the numerical values but explain how they compare for both dealerships NORMAL DISTRIBUTION What is the empirical rule tell you? What is the equation relating Z-score to Mean, standard deviation, and your value of X? SWIM TEAM TIMES The times for the 100m freestyle for the womens swim team is evenly distributed with a mean of 59.6 sec. and a standard deviation of 1.2 seconds. a) b) c) d) e) What time can 50% of the teammates complete a 100m freestyle in? What percent of swimmers can complete a 100m freestyle between 58.4 seconds and 60.8 seconds. Jane brags that she can swim the race faster than 97.5% of her teammates? What would her time be? If Jenny is wanting to make the team and she can swim a 100 m freestyle in 61 seconds, do you think she would make the team? What is the probability that one of the girls will beat the opponents fastest swimmer that can swim a 100 m freestyle in 56 seconds? Z-SCORE What does a z-score tell you? USING Z SCORES P (Z < 1.5) b) P(Z < z) = 0.35 c) P (Z > - 1) d) P (|Z| < 1.2) e) P(Z > z) = 0.60 f) P (Z > 0.5) g) P (-1 ≤ Z ≤ 1.5) h) P(-z < Z < z) = .78 a) BOX OFFICE SALES Opening weekend, Marvel films gross sales are normally distributed making an average of $68,326,910 and a standard deviation of $22,442,000. a) X-men only made $55,101,604, how many standard deviations does this movie fall from the mean. b) Thor: The Dark World had an opening box office sales of $85,737,841. What percentile does Thor2 fall under c) The Avengers made $207,438,708. What percentile does this fall under d) If the new spiderman is hoping to hit at least the 40th percentile, how much money is it expecting to make opening weekend in gross sales?