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Empirical Rule

Empirical Rule

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Based on the Empirical Rule, answer the following questions. 1. What is the probability that data is between one standard deviations below the mean (-lo) and two standard deviations above the mean (20)? 16% 2.5% -40 -30 -20 -10 1o 20 30 40 Start by drawing a normal curve, then label the horizontal axis with the mean, u, in the center and three standard deviations on mean. The standard deviations to the left of the mean are negative and the standard deviations to the right of the mean are positive. We know that the area under the curve is 1. To find the area of the shaded region, subtract the areas that we know. We know that the area to the left of -lo is 16% and the area to the right of 20 is 2.5%.. 1 – 0.16 – 0.025 = 0.815 = 81.5%. The area is the same as the probability, which is 81.5%. sides of the 2. What is the probability of the data is within 2 standard deviations of the mean? Draw a normal curve and then find the probability. The probability is %. Click to view explanation 3. What is the probability of the data to the left of u? Draw a normal curve and then find the probabilities. The probability is %. Click to view explanation 4. What is the probability of the data between the mean and the third standard deviation? Draw a normal curve and find the probability. The probability is % Click to view explanation
Transcribed Image Text:Based on the Empirical Rule, answer the following questions. 1. What is the probability that data is between one standard deviations below the mean (-lo) and two standard deviations above the mean (20)? 16% 2.5% -40 -30 -20 -10 1o 20 30 40 Start by drawing a normal curve, then label the horizontal axis with the mean, u, in the center and three standard deviations on mean. The standard deviations to the left of the mean are negative and the standard deviations to the right of the mean are positive. We know that the area under the curve is 1. To find the area of the shaded region, subtract the areas that we know. We know that the area to the left of -lo is 16% and the area to the right of 20 is 2.5%.. 1 – 0.16 – 0.025 = 0.815 = 81.5%. The area is the same as the probability, which is 81.5%. sides of the 2. What is the probability of the data is within 2 standard deviations of the mean? Draw a normal curve and then find the probability. The probability is %. Click to view explanation 3. What is the probability of the data to the left of u? Draw a normal curve and then find the probabilities. The probability is %. Click to view explanation 4. What is the probability of the data between the mean and the third standard deviation? Draw a normal curve and find the probability. The probability is % Click to view explanation
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