Statistics & Probability Activity Sheet 4 NORMAL PROBABILITY DISTRIBUTIONS Learning Competencies: M11/12SP-IIIe-d-1 At the end of the activity, the learner is expected to 1. Computes probabilities and...

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Extracted text: Statistics & Probability Activity Sheet 4 NORMAL PROBABILITY DISTRIBUTIONS Learning Competencies: M11/12SP-IIIe-d-1 At the end of the activity, the learner is expected to 1. Computes probabilities and percentiles using the standard normal table. Solve the following problems. Show complete solutions. 1. Sleeping Times of Medical Residents: The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, with a mean of 6.1 hours and a standard deviation of 1.0 hour. a. What is the shortest time spent sleeping that would still place a resident in the top 5% of sleeping times? 2. The annual per capita consumption of fresh bananas (in pounds) can be approximated by a normal distribution, with a mean of 10.4 pounds and a standard deviation of 3 pounds. a. What is the smallest annual per capita consumption of bananas that can be in the top 10% consumptions? b. What is the largest annual per capita consumption of bananas that can be in the bottom 5% of consumptions? 3. Statistics Grades: In a large section of statistics class, the points for the final exam are normally distributed, with a mean of 72 and a standard deviation of 9. Grades are assigned according to the following rule. The top 10% receive A's. The next 20% receive B's. The middle 40% receive C's. The next 20% receive D's. The bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, B, C, and a D. 4. Sunflowers: An experiment publishing in the Annals of Botany investigated whether the stem diameters of the dicot sunflower would change depending on whether the plant was left to sway freely in the wind or was artificially supported. Suppose that the unsupported stem diameters at the base of a particular species of sunflower plant have a normal distribution with an average diameter of 35 millimeters and a standard deviation of 3 mm. a. What is the probability that a sunflower plant will have a based diameter of more than 40 mm? b. If two sunflower plants are randomly selected, what is the probability that both will have a basal diameter of more than 40 mm? c. What diameter represents the 90th percentile of the distribution of diameters? MYP20-2021