Question

In: Statistics and Probability

(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a...

(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are

z₃ ≈ −1.101,

z₄ ≈ −0.944,

z₉ ≈ −0.157,

z₁₄ ≈ 0.629,

and z₂₀ ≈ 1.573.

Find the mean and the standard deviation of these z-scores.

mean
standard deviation

(b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a standard deviation of 8.226. The z-scores for each of the six data values are

z₂ ≈ −1.459,

z₆ ≈ −0.973,

z₁₂ ≈ −0.243,

z₁₇ ≈ 0.365,

z₂₂ ≈ 0.973,

and z₂₅ ≈ 1.337.

Find the mean and the standard deviation of these z-scores.

mean
standard deviation

(c) Use the results of part (a) and part (b) to make a conjecture about the mean and standard deviation of the z-scores for any set of data.

The mean and standard deviation of z-scores are never the same.The mean of the z-scores is always 1, and their standard deviation is 0. The mean of the z-scores is always 1 more than the standard deviation.The mean of the z-scores is always 0, and their standard deviation is 1.

Expert Solution

(a)

(b)

(c) The mean of the z-scores is always 0, and their standard deviation is 1.

orchestra answered 2 years ago

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