The following items 6 - 8 are not related to Problem I above. If a population di

Question

The following items 6 - 8 are not related to Problem I above. If a population distribution is skewed to the right, then, given a random sample from that population, would expect that: A. The median would be greater than the mean. B. The mode would be equal to the mean. C. The median would be less than the mean. D. The median would be equal to the mean. According to Chebyshev's rule, at least ______ percent of the observations in a sample are contained 3 standard deviations around the mean, regardless of the shape of the distribution. A. 93.75 B. 88.89 C. 75.00 D. 66.67 According to the empirical rule, if the data form a normal distribution, ____ percent of the observation sample are contained within 2 standard deviations around the mean. A. 95 44 B. 93.75 C. 88.89 D. 68.26

Explanation / Answer

6.

since in right skewed distribution mean shifted to right

while median is middle value so

mean > median

7.

given 3 sigma around the mean

so k=3

hence

at lest 1-(1/k2)

so required probability =1- 1/k2 =1 -1/9 =8/9 =0.88888

hence 88.89%

8) according to empirical rule 95% of population fall within 2sd

hence

95.44 ans

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