There 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 99 and a standard deviation of 21 . Complete the following statements about the distribution of scores on this personality test.
(a) According to Chebyshev's theorem, at least----- of the scores lie between 57 and 141.
(b) According to Chebyshev's theorem, at least 36% of the scores lie between ----and----- . (Round your answer to the nearest integer.)
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between -----and ------.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately------- of the scores lie between 57 and 141.
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