Suppose X~N(53,6). Use the Empirical Rule to answer the following questions.

Question

What percent of data lies between 41 and 65?

(b) What percent of data lies between 53 and 59?

(c) 99.7% of data lies between 𝑥 =__________ and 𝑥 = __________.

Answer 1

Data is normally distributed with mean 53 and standard deviation 6.

41 is 2 standard deviations (2*6=12) below the mean of 53

65 is 2 standard deviations (2*6=12) above the mean of 53.

Per the empirical rule 95% of the data lies within 2 standard deviations of the mean. Answer 95%

Per the empirical rule 99.7% of the data is within 3 standard deviations of the mean

35 is 3 standard deviations (3*6=18) below the mean of 53

71 is 3 standard deviations (3*6=18) above the mean of 53. Answer 35 to 73