AP Statistics - Unit 1 Progress Check MCQ Part B latest solution 2024 A+ QUALITY.

AP Statistics - Unit 1 Progress Check MCQ Part B latest solution A+ QUALITY A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco weighs 8 pounds. A cat's weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the following is the best description of Gordo's and Flaco's weights? - Gordo's weight is classified as unhealthy but Flaco's weight is not. WHY? Because Gordo's weight is over 3 standard deviations above the mean, his weight is in the top 5% of all weights and is classified as unhealthy. Flaco's weight is less than 2 standard deviations below the mean, so his weight is not in the bottom 5% of all weights and is not classified as unhealthy. In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all daily high temperatures are between 83°F and 89°F. What is the standard deviation of the distribution? - 1.5°F WHY? The empirical rule states that approximately 95% of the observations in a data set that is approximated by a normal curve will lie within 2 standard deviations of the mean. Since 95% of all daily high temperatures are between 83°F and 89°F, the interval from 83°F to 89°F has a width of 4 standard deviations (2 above the mean and 2 below the mean). So 1 standard deviation is (89−83)/4 = 1.5°F Researchers studying catfish estimated the number of fingerling catfish and large catfish living in different rivers throughout the country. The following histograms summarize the relative frequency for each type of catfish. Based on the histograms, which of the following is the best comparison of the means and the ranges for the two distributions? - The mean and range of the fingerling catfish are both greater than those of the large catfish. WHY? The range of the distribution of fingerling catfish is between 6,000 and 8,000, while the range of the distribution of large catfish is between 1,500 and 2,000. Therefore the range of the distribution of fingerling catfish is greater than the range of the distribution of large catfish. The least value in the distribution of fingerling catfish is more than the greatest value of the distribution of large catfish. Therefore the mean of the distribution of fingerling catfish must be greater than the mean of the distribution of large catfish.