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zeinab kourouma Date : 6 1 02125 Name : Unit 7 CABS 2 Quick Review 1. Use the normal curve to fill in the blanks describing how the proportions relate to the areas under the normal curve . 58% 95% 99 7% -30 -20 -10 10 20 30 About of the values fall within one standard deviation of the mean. About of the values fall within two standard deviations of the mean. About (almost all) of the values fall within three standard deviations of the mean. 2. When Lin drives a golf ball, it travels a mean distance of 200 yards with a standard deviation of 20 yards, and the distribution of lengths is approximately normal. Approximately what percentage of her shots will travel less than 220 yards? a. 0.025 b. 0.16 c. 0.32 d. 0.68 e. 0.84 f. 0.95 3. Select all the properties of a normal distribution. The distribution is skewed. b. The distribution is determined by the mean and standard deviation. c. The distribution has a height of zero when it is more than 5 standard deviations away from the center. d. The distribution is centered at the mean. The total area under the normal distribution curve is 10. f. The area under the normal distribution curve and within 1 standard deviation of the center is about 68% of the total area under the curve. 9. The distribution is bell-shaped. 4. A distribution of weights (Ibs.) is approximately normal with a mean of 18.5 lbs. and a standard deviation of 1.5 Ibs. Assuming the weights are normally distributed, estimate the proportion of weights that are less than 15.5 Ibs.5. A high school offered an ACT prep class this past year. It was offered in two different formats: online or classroom teacher. The counselors wanted to know which teaching method yielded higher ACT scores, so they planned an experiment to compare ACT scores of students between the two formats at the end of class. 62 students signed up to take some form of the ACT prep class. a . Explain why an experimental study would be better than a survey or observational study in this situation. . Describe a way that would assign the 62 students into the two groups that would allow the counselor to answer the question of interest. c. The distribution of scores for the group taking the online ACT prep is shown. ACT Composite Scores Mean = 21, standard deviation = 3.45 Why is it reasonable to model this distribution with a normal distribution? Number of Students 20 35 ACT Composite Score d. Assuming this group of students is representative of all students who could be taking the online ACT prep, use a normal distribution to estimate the probability that a randomly selected student could score 30 or above using the online ACT prep. e. The group taking the ACT prep with a teacher had a mean score of 20.6 and a standard deviation of 4.3. Write a sentence or two that summarizes any conclusions that can be made about the statistical question, "Does taking an online ACT prep course improve scores more than taking an ACT prep course with a teacher?"