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11/5/2017
Ryan
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Hi,Thank you for using the site. Please post the question information. I will take a look at immediately.Thanks,Ryan
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Customer reply replied 6 months ago
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 (______).
Thanks. I'll get the answers back to you in just a few minutes.
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Thank you for your patience. Here are the solutions:

(a) The values 60 and 156 are within 2 standard deviations of the mean. According to Chebyshev's Theorem, the percentage of values between these two limits is 1 - (1/2)^2 = 1 - 1/4 = 3/4 = 75%.

(b) The values 72 and 144 are within 1.5 standard deviations of the mean. According to Chebyshev's Theorem, the percentage of values between these two limits is 1 - (1/1.5)^2 = 1 - (2/3)^2 = 1 - 4/9 = 5/9 ≈ 56%.

(c) The values 60 and 156 are each 2 standard deviations from the mean. According to the Empirical Rule, 95% of the values will be between these limits.

(d) According to the Empirical Rule, 99.7% of the scores will be within 3 standard deviations of the mean. For this distribution those limits are 108 - 3(24) = 36 and 108 + 3(24) = 180.

Please feel free to ask if you have questions about any of these solutions.

Thanks,

Ryan

Ryan
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Customer reply replied 6 months ago
Thank you.

You're welcome. Thank you for the high rating.

If there is anything else that I can help you with in the future, please feel free to request me. You can do so by simply adding "For Ryan" at the beginning of your new question.

Thanks again,

Ryan

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Customer reply replied 5 months ago
Hello, I have added another question for you. The Order ID is 18205023-380. If at all possible, I would need it answered by tomorrow 12/1. Please let me know if I should seek another expert for assistance. Thank you
Hi. I’ll try to take a look at it later when I have access to my laptop. The phone app that I am using now doesn’t show me any of your other open questions.
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