There are dozens of personality tests available on the World Wide Web


There are dozens of personality tests available on the World Wide Web

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There are dozens of personality tests available on the World Wide Web. One test, scored on a scale of to , 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 and a standard deviation of . 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 51.5 and 166.5 .



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

of the scores lie between 63 and 155 .



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

of the scores lie between 63 and 155 .



(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between ? and ?

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