0.. X MDS_2022_Chapter2Practicepdf @ I'll / E AP Statistics Practice: Chapter 2 7'. A sleep time of 15.9 hours per day for a newborn baby is at the 10lh percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies? 8. The Montana Livestock Association reports that weights of 3-year old cows are normally distributed with mean,u: 1 152, and standard deviation,cr= 84. a) How many standard deviations below the mean would a cow weight 1000 pounds be? b) What is more likely a cow weighing under 1000 pounds or a cow weighing over 1325 pounds ? c) What weight would you consider to be unusually high for a 3-year old cow? Explain your reasoning. 9. A forest ranger has measured the diameters of oak trees in a national park for many years and has sufcient evidence to believe that the distribution of diameters follows a Normal Distribution with a mean of 10.4 inches and a standard deviation of 4.7 inches. a) What size diameters would you expect to serve as the middle 95% of the data? b) What percent of trees would be less than 2 inches in diameter? c) What percent of trees would you expect to be between 5.7 and 10.4 inches in diameter? d) What percent of trees should exceed 15 inches in diameter? 10. The distribution of scores on a recent test closely followed a Normal distribution with a mean of 22 points and a standard deviation of 4 points. a. What proportion of the students scored at least 25 points on this test? b. What is the 3151 percentile of the distribution of test scores? I; The teacher wants to transform the test scores so that they have an approximately Normal distribution with a mean of 80 points and a standard deviation of 10 points. To do this, she will use a formula in the form new score=a+b (old scamw) Find the values of a and b that the teacher should use to transform the distribution of test scores. d. Before the test, the teacher gave a review assignment for homework. The maximum score on the assignment was 10 points. The distribution of scores on this assignment had a mean of 9.2 points and a standard deviation of 2.1 points. Would it be appropriate to use a Normal distribution to calculate the proportion of students who scored below 7 points on this assigmnent? Explain your answer. AP Statistics Practice: Chapter 2 AP Statistics Practice: Chapter 2 An airline ies the same route at the same time each day. The ight time varies according to a Normal distribution with unknown mean and standard deviation. On 15% of days, the ight takes more than an hour. On 3% of days, the ight lasts 75 minutes or more. Determine the mean and standard deviation ofthe ight time distribution. The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Determine the mean and standard deviation of the distribution. Given a Normal distribution with 80% of the values above 125 and 90% of the values above I 10, what are the mean and standard deviation? At the end of the semester, a professor determines the percent grade earned by students, taking into account all homework, tests, and project scores. These student scores are Normally distributed with a mean of 75 and a standard deviation of 8. A standard lO-point scale is used to determine letter grades. a. What percentage of students fail the course? b. What percentage of students earn an A? c. What percentage of students earn a B? d. If the teacher changes the structure and decides to give As to the top 10% of the class, then what is the cutoff point for an A? e. If the teacher then decides to give Bs to the next 20% of the class, what are the cutoff points for a B? 2of4