1230 HHOduction to Statistics (Spring 2016) 3, A group of rescarchers want to ex

Question

1230 HHOduction to Statistics (Spring 2016) 3, A group of rescarchers want to examine a relationship between students' motivation level and their class performance. They measured 520 ASU students on their motivation level and found the motivation level is normally distributed. They transformed the original motivation scores into the corresponding z-scores. (1) For a study they want to examine students who are not motivated. If they want to recruit students whose motivation scores are in the bottom 4%, what z-score would be the cut-off value that separates the bottom 4% from the rest? (2) For another study, they want to examine students who are moderately motivated. If they want to recruit students whose motivation scores are in the middle 60%, what z-scores would be the cut-off values that separate the middle 60% from the rest?

Explanation / Answer

Part 1

Prob =0.04

Hence Z is that value which would give 0.04 as the cumulative probability = -1.751

Part 2

Middle values are 60% implies the edges are 20% and 80% which gives the

Z scores as 0.8416 and -0.8416

Part 3

This cannot be solved as we donot know what the mean or the standard deviation of the sample is

If we know what the mean and sample deviation is.

Then find the Z=(x-mean)/stddev gives whats your Z score

Now using the Z table,find what is the value of the P(Z) .Hence the proportion>ur score=1-P(Z)

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