Answer to Question #291958 in Python for Karan

Question

A normal distribution which has a mean of 50 and standard deviation of 7 is takeninto consideration. 68% of the distribution can be found between what two numbers? a. 40 and 60 b. 0 and 43 c. 0 and 68 d. 43 and 57

Answer 1

The Empirical RuleIf X is a random variable and has a normal distribution with mean µ and standard deviation σ, then the Empirical Rule states the following:

• About 68% of the x values lie between –1σ and +1σ of the mean µ (within one standard deviation of the mean).

About 68% of the x values lie between –1σ = (–1)(7) = –7 and 1σ = (1)(7) = 7 of the mean 50. The values 50 – 7 = 43 and 50 + 7 = 57 are within one standard deviation from the mean 50. Therefore our distribution will be between 43 and 57