Question

On a measure with a mean of 10 and a standard deviaton of 2, Sumathi scored...

On a measure with a mean of 10 and a standard deviaton of 2, Sumathi scored 13. What proportion of people score farther from the mean than Sumathi?

(Give your answer to at least 3 places past the decimal point). The answer is NOT 0.433. Farther from the mean than 13, which includes everyone with a score >13 and everyone with a score <7, because 7 is also 1.5 SD from the mean.

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Answer #1

Solution:

Given in the question

mean = 10

Standard deviation = 2

We need to calculate that P(Xbar>13) + P(Xbar<7)

Z = (13-10)/2 = 1.5

Z = (7-10)/2 = -1.5

From Z table we found P-value

P(Xbar>13) + P(Xbar<7) = 1- P(Xbar<13) + P(Xbar<7) = 1- 0.9332 + 0.0668 = 0.0668 + 0.0668 = 0.1336

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