54.5 58 61.5 65 68.5 72 75.5 -30 -20 -10 10 20 30 Heights of Adult Females (inches) 10) A researcher recorded the birth weights of a sample of newborn babies. The average birth weight was 7.2 pounds and the standard deviation was 0.9 pound. Assume that the birth weights follow a normal distribution. a. Sketch and label a normal curve. Include 3 standard deviations above and below the mean. b. Determine the percent of newborns that weighed between 2 standard deviations below the mean and 2 standard deviations above the mean. c. Determine the percent of newborns that weighed less than the mean. d. Determine the percent of newborns that weighed between 1 standard deviation above the mean and 3 standard deviations above the mean. 11) Mr. Giordano's Math class took a quiz last week. The mean quiz score was 87% and the scores had a SD of 5 points. JJ earned the highest score on the quiz with a 95%. a. How many standard deviations away from the mean was JJ's quiz score? b Based on your calculation, is the distribution of scores approximately normal? Why or why not? 12) Mr. Sellers' Math 2 class took the same quiz. The mean score was 82% and the scores had a SD of 3 points. The highest score on the quiz was a 91 and the lowest score was a 73. Statistics CP/Honors a. Name: Is the distribution of Mr. Sellers' quiz scores approximately normal? Why or why not? b. What percent of students scored below 79%? c. What percent of students scored above 88%? d. What percent of students scored between 79% and 88%? HONORS ONLY: These measurements describe the usable capacity (in cubic feet) of a sample of 36 side-by-side refrigerators. 13) What is the shape of the distribution? How do you know? 12.9 13.7 14.1 14.2 14.5 14.5 14.6 14.7 15.1 15.2 15.3 15.3 15.3 15.3 15.5 15.6 15.6 15.8 16.0 16.0 16.2 16.2 16.3 16.4 16.5 16.6 16.6 16.6 16.8 17.0 17.0 17.2 17.4 17.4 17.9 18.4 Mean SD Min Q Med Q Max 36 15.825 1.217 12.9 15.15 15.9 16.6 18.4 14) Is the data normally distributed? Let's find out! We'll find the percent of data within 1, 2, and 3 standard deviations. If they match the percentages of the empirical rule, then it's a normal distribution! Use the summary statistics and the list of fridge measurements to complete the calculations. How big is a fridge that's 1 SD below the mean? Count how many data points are between those values: How big is a fridge that's 1 SD above the mean? What percentage of the data is that? How big is a fridge that's 2 SD below the mean? Count how many data points are between those values: How big is a fridge that's 2 SD above the mean? What percentage of the data is that? How big is a fridge that's 3 SD below the mean? Count how many data points are between those values: How big is a fridge that's 3 SD above the mean? What percentage of the data is that? Statistics CP/Honors Name: Copy down the percentages you just calculated so you can compare them to the percentages of a normal distribution: Percentage of fridge data w/in 1 SD of mean: Percentage of fridge data w/in 2 SD of mean: Percentage of fridge data w/in 3 SD of mean: Empirical Rule 68% 95% 99.7% 15) Based on your answers to Questions 13 and 14, is the distribution of usable capacity for these refrigerators approximately normal? Explain your answer. For Questions 16 and 17, assume that the population distribution of usable capacity in side-by-side refrigerators is approximately normal with mean 16 cubic feet and standard deviation 1.2 cubic feet. 16) About what proportion of side-by-side refrigerators have a usable capacity between 13.6 and 19.6 cubic feet? Justify your answer. 17) Find and interpret the 16th percentile of this distribution.