The 68-95-99.7 Rule states that 68% of a normal distribution's values are within one standard deviation of the mean. 95% are within two standard deviations and 99.7% are within three standard deviations. Show
A. C. B. D. 10. What percent of the area under a normal curve is within standard deviations? C. B. A. D. 11. What is the area if the z - score given is ? A. C. B. D. 12. What is the z-value if the area is ? A. C. B. D. 13. Using the standard normal curve, what is the approximate area of A. C. B. D. 14. The weights lin kgi of 11-STEM B follow a normal distribution and has a mean of and A. a standard deviation of . How many students have weights greater than ? C. B. D. 15. What is the value of percentile in a standard normal distribution? A. B. C. D. For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean; 95% lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean. Areas under portions of a normal distribution can be computed by using calculus. Since this is a non-mathematical treatment of statistics, we will rely on computer programs and tables to determine these areas. Figure 1 shows a normal distribution with a mean of 50 and a standard deviation of 10. The shaded area between 40 and 60 contains 68% of the distribution.  Figure 1. Normal distribution with a mean of 50 and standard deviation of 10. 68% of the area is within one standard deviation (10) of the mean (50). Figure 2 shows a normal distribution with a mean of 100 and a standard deviation of 20. As in Figure 1, 68% of the distribution is within one standard deviation of the mean. Figure 2. Normal distribution with a mean of 100 and standard deviation of 20. 68% of the area is within one standard deviation (20) of the mean (100). The normal distributions shown in Figures 1 and 2 are specific examples of the general rule that 68% of the area of any normal distribution is within one standard deviation of the mean. Figure 3 shows a normal distribution with a mean of 75 and a standard deviation of 10. The shaded area contains 95% of the area and extends from 55.4 to 94.6. For all normal distributions, 95% of the area is within 1.96 standard deviations of the mean. For quick approximations, it is sometimes useful to round off and use 2 rather than 1.96 as the number of standard deviations you need to extend from the mean so as to include 95% of the area. Figure 3. A normal distribution with a mean of 75 and a standard deviation of 10. 95% of the area is within 1.96 standard deviations of the mean. The normal calculator can be used to calculate areas under the normal distribution. For example, you can use it to find the proportion of a normal distribution with a mean of 90 and a standard deviation of 12 that is above 110. Set the mean to 90 and the standard deviation to 12. Then enter "110" in the box to the right of the radio button "Above." At the bottom of the display you will see that the shaded area is 0.0478. See if you can use the calculator to find that the area between 115 and 120 is 0.0124. Figure 4. Display from calculator showing the area above 110. Say you wanted to find the score corresponding to the 75th percentile of a normal distribution with a mean of 90 and a standard deviation of 12. Using the inverse normal calculator, you enter the parameters as shown in Figure 5 and find that the area below 98.09 is 0.75. To one decimal place, what percentage of the area under the normal curve lies between #+-# 2 standard deviations of #mu#?Statistics 1 AnswerShwetank Mauria Nov 9, 2016 Area under the normal curve between#+-2#standard deviation is#95.45%#. Explanation:Area under the normal curve between#+-1#standard deviation is#68.27%# between#+-2#standard deviation is#95.45%# between#+-3#standard deviation is#99.73%# Answer link Related questions
Impact of this question2900 views around the world You can reuse this answer What percent of the area under a normal curve is within standard deviation?For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean; 95% lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.
What is the area of the normal curve from one standard deviation?68% of the area is within one standard deviation (20) of the mean (100). The normal distributions shown in Figures 1 and 2 are specific examples of the general rule that 68% of the area of any normal distribution is within one standard deviation of the mean.
What percentage of the area under the curve is within one standard deviation of the mean on either side of the mean )?Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95% of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.
What is the area of the standard normal curve in percent?The standard normal distribution is a probability distribution, so the area under the curve between two points tells you the probability of variables taking on a range of values. The total area under the curve is 1 or 100%.
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What percent of the area under a normal curve is within a standard deviation?
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