A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of20

to80

.In a recent year, the national mean score for the writing section was49.6

,with a standard deviation of9.3

. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.

(a) According to Chebyshev's theorem, at least?

56%

75%

84%

89%

of the scores lie between 31.0 and 68.2.

(b) According to Chebyshev's theorem, at least 8/9 (about 89%) of the scores lie between24.0

and36.0

. (Round your answer to 1 decimal place.)

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between29.0

and69.6

.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately?

68%

75%

95%

99.7%

of the scores lie between 31.0 and 68.2.