Question

Oprah looks at this histogram of a distribution with a mean of 6.7 grams

and a standard deviation of 1 gram. She claims that approximately 68% of
the data is between 5.7 and 7.7 grams. What is the error in her thinking?

Answer 1

68% of the data is between 5.7 and 7.7 grams.

Explanation:

According to the empirical rule for a normal distribution, 68% of data falls within one standard deviation, 95% of data falls within two standard deviation and 99.7% of data falls within three standard deviation.

Given that:

mean (μ) = 6.7 grams, standard deviation (σ) = 1 gram.

From the empirical rule:

68% of the data is between one standard deviation i.e μ ± σ = 6.7 ± 1 = 5.7, 7.7

Therefore 68% of the data is between 5.7 and 7.7 grams.