Chebyshev's theorem and the empirical ruleThere are dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200, is designed to give an indication of how "personable" the test taker is, with higher scores indicating more "personability."
Suppose that scores on this test have a mean of 108 and a standard deviation of 24. Complete the following statements about the distribution of scores on this personality test.
(a) According to Chebyshev's theorem, at least (56%, 75%, 84%, 89%) of the scores lie between 60 and 156.
(b) According to Chebyshev's theorem, at least (56%, 75%, 84%, 89%) of the scores lie between 72 and 144.
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately (69%, 75%, 95%, 99.7%) of the scores lie between 60 and 156.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the scores lie between (_____) and (______).
6 years ago
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