The ages of a town in central Florida were recorded. The mean age of the populat

Question

The ages of a town in central Florida were recorded. The mean age of the population of the town was found to be = 60 with a standard deviation of = 4.3. Using this information please answer the following questions.

What z-score cuts of the top 10% of this (or any) distribution?

What raw score cuts off the top 10% of this distribution?

What raw scores mark the middle 60% of this distribution?

What raw score corresponds to a z-score of 0.00?

What raw score corresponds to a z-score of -1.51?

What raw score corresponds to a z-score of 68.7? Does it seem likely that we would find someone with that z-score?

Explanation / Answer

The ages of a town in central Florida were recorded. The mean age of the population of the town was found to be = 60 with a standard deviation of = 4.3. Using this information please answer the following questions.

What z-score cuts of the top 10% of this (or any) distribution?

P(Z >z) = 0.10

z = 1.282

What raw score cuts off the top 10% of this distribution?

X = mean + z* sd =60 +1.282 * 4.3 = 65.5126

What raw scores mark the middle 60% of this distribution?

P(-z < Z < z) = 0.6

z = 0.841

X = 60 +4.3 * 0.841 = 63.6163

What raw score corresponds to a z-score of 0.00?

X = 60

What raw score corresponds to a z-score of -1.51?

Z = 60 + 1.282 * (-1.51) = 58.06418

What raw score corresponds to a z-score of 68.7? Does it seem likely that we would find someone with that z-score?

z = (X - mean)/sd = (68.7 - 60)/4.3 = 2.02325

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