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?

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

Step-by-step 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.

The probability of success is 0.276.

Step-by-step explanation:

since 55% of the students are enrolled in an introductory statistics class this semester are freshmen.  the probabilities of exactly 2 freshmen is statistically independent, meaning we gonna use the binomial distribution.

In the binomial distribution:

n = 5, p = 0.55, x = 0, 1, 2, 3, 4, 5.

Probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen is:

P(X = 2) = [5!/2!(5 - 2)!]*(0.55)^(2)*(0.45)^3

             = 0.2756

Therefore, The probability of success is 0.276.