Use the Empirical Rule (68-95-99.7 Rule) to estimate the following probabilities
ID: 2936198 • Letter: U
Question
Use the Empirical Rule (68-95-99.7 Rule) to estimate the following probabilities. measurement from a Normal distribution a. 6. Assume x is a Find the probability that a value x is more than 2 standard deviations above the mean. b. Find the probability that a value x is more than 1 standard deviation below the mean. Find the probability that a value x is between 1 standard deviation above the mean and 2 standard deviations below the mean. c. d. Find the probability that a value of x is more than 3 standard deviations above the mean or 3 standard deviations below the mean (this is the probability that X is in the two tails of the distribution, in the lower tail or the upper tail.) Find the probability that a value of x is between the mean and 1 standard deviation below the mean e.Explanation / Answer
According to 68-95-99.7 rule, the proportion of data that lies between 1,2 and 3 standard deviations from mean for normally distributed data is 68%, 95% and 99.7%
a) P(x is more than 2 standard deviation from mean) = (1 - 0.95)/2 = 0.025
b) P(x is more than 1 standard deviation below mean) = (1-0.68)/1 = 0.16
c) P(x is more than 1 standard deviation above mean and 2 standard deviations below mean)
= (0.95 + 0.05/2) - (0.32/2)
= 0.815
d) P(more than 3 standard deviations above mean or 3 standard deviations below mean) = 1 - 0.975
= 0.025
e) P(mean is between the mean and 1 standard deviation below the mean)
= 0.68/2
= 0.34
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