i have two two judges convicting a robberer judge a mean is 33.0 and standard deviation is 2.0. judge b has a mean of 30.0 and a standard deviation of 8.1. which judge would the robber want to sentence?

Answer 1

I assume the values are the number of years in sentence. Although judge A has a higher mean value, judge B has greater variability. Calculate the Z score for a sentence of 33 from judge B.

Z = (score-mean)/SD = (33-30)/8.1 = ?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion higher than that Z score.

Judge A has only .025 probability of giving sentence of 37 years or more (approximately 2 SD above the mean).

What would that probability be for judge B?

Z = (score-mean)/SD = (37-30)/8.1 = ?

Use the same table to make your decision.