A roller coaster in the Kiddie World amusement park is designed to fit children of a specific size range. 12. The heights of 5-year old boys in the United States are approximately normally distributed with a mean of (f) 42.65 inches and a standard deviation of (g) 2.25 _ inches. Label the normal curve below to show the complete distribution of heights out to four standard deviations in each direction of the mean. (3 pt) The roller coaster fits children from 36 inches to 48 inches tall, so children shorter than 36 inches or taller than 48 inches won't be allowed to ride it. 13-a What is the z-score of a 5-year old boy who is 36 inches tall? Show your calculations. Round to one decimal place. (4 pt) 13-b What percentage of 5-year old boys have heights below 36 inches? (too short to ride the coaster). Do not round. Refer to the z-table that was included with the Stats 3 handout. (2 pt) 14-a What is the z-score of a 5-year old boy who is 48 inches tall? Round to one decimal place. (4 pt) 14-b What percentage of 5-year old boys have heights above 48 inches? (too tall to ride the coaster). Do not round. Refer to the z-table that was included with the Stats 3 handout. (4 pt) 15 What percentage of 5-year old boys will be allowed to ride the roller coaster? Do not round. (4 pt) 16 Assume there are 4.7 million 5-year old boys in the United States. How many of the boys are the right height to fit on the coaster (36 in to 48 in tall)? Round your results to the nearest thousand boys. Show your calculations. Label your result. (4 pt) Part 4 - Interpreting Survey and Poll Results (Margins of Error, Confidence Intervals) (Questions 17-20) 17-18. A local school used a survey to ask high school students whether or not they like the school's current mascot, which is a tiger. 17. Among seniors, (h) 19-20. A month before the election, local residents were polled to see who their preference was in the upcoming mayoral race between Candidate O'Brien and Candidate Riegel. Those who participated were also asked to disclose their age and classified as either under or over 40 years old. For each age group, identify the projected winner or state the race is too close to call. Assume both age groups have a margin of error of 3.2 percentage points. was (i) 4.8_ 55.9 % said they like having a tiger as the school's mascot. The margin of error percentage points. 19a 17a Calculate a confidence interval for the true percentages of seniors who like having a tiger as the school's mascot. Show your calculations. (3 pt) In the spaces provided show all relevant calculations. Explanations should be in complete sentences. (1) 47.1 % of residents under age 40 support Candidate O'Brien. Calculate a confidence interval for the true percentage of residents under age 40 who support Candidate O'Brien. (3 pt) 19b (m). 41.5 % of residents under age 40 support Candidate Riegel. Calculate a confidence interval for the true percentage of residents under age 40 who support Candidate Riegel. (3 pt) 17b Can we conclude that the majority of seniors like having a tiger as the school's mascot? Why or why not? (3 pt) 19c Among residents under age 40, is there a projected winner or should this race be considered too close to call? If there is a projected winner, state who it would be. Explain your conclusion by referencing your confidence intervals. (3 pt) 18. Among juniors, (j) error was (k) 4.1 52.0 % said they like having a tiger as the school's mascot. The margin of percentage points. 20a (n) 35.6 % of residents over age 40 support Candidate O'Brien. Calculate a confidence interval for the true percentage of residents over age 40 who support Candidate O'Brien. (3 pt) 18a Calculate a confidence interval for the true percentages of juniors who like having a tiger as the school's mascot. Show your calculations. (3 pt) 20b (o). 45.1% of residents over age 40 support Candidate Riegel. Calculate a confidence interval for the true percentage of residents over age 40 who support Candidate Riegel. (3 pt) 18b Can we conclude that the majority of juniors like having a tiger as the school's mascot? Why or why not? (3 pt) 20c Among residents over age 40, is there a projected winner or should this race be considered too close to call? If there is a projected winner, state who it would be. Explain your conclusion by referencing your confidence intervals. (3 pt)