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Chapter 2: Q94E (page 116)

Suppose that 40 and 90 are two elements of a population data set and that their z-scores are -2 and 3, respectively. Using only this information, is it possible to determine the population鈥檚 mean and standard deviation? If so, find them. If not, explain why it鈥檚 not possible.

Short Answer

Expert verified

Yes, it is possible to find the mean and the standard deviation.

The mean is 60.

The standard deviation is 10.

Step by step solution

01

Given information

x = 40, and x = 90.

The z-score for 40 is (-2), and the z-score for 90 is 3

02

Finding the mean and the standard deviation

As we have two values from the population, it is possible to calculate the mean and the standard deviation.

z-score=虫-渭蟽WhenZ=-2,-2=40-渭蟽WhenZ=3,3=90-渭蟽Sowecanalsowritetwoequationsmentionedaboveasfollows:-2蟽=40-渭3蟽=90-渭Now,bysubtractingtheequations,weget-2蟽-3蟽=40-渭-90-渭-5蟽=-50蟽=505蟽=10

Therefore, the standard deviation is 10.

Substituting the value of 蟽 in 3蟽 = 90 - 碌, we get

3脳10=90-渭30=90-渭渭=90-30渭=60

Therefore, the mean is 60.

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