Question

george’s average bowling score is 180; he bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. bill’s average bowling score is 190; he bowls in a league where the average is 160 and the standard deviation is 15. who ranks higher in his own league, george or bill?

Answer 1

Bill is better bowler than George.

To decide who's the relative better bowler, George or Bill, I've first drawn bell curves for each of their leagues. George's league is in red mean is 150 a standard deviation of 20. And Bill's League Demean is higher at 160, but the standard deviations it is lower at 15, so I've numbered my bell curve by 15.

Now to decide who's relative better bowler, I'm going to calculate their Zscores for George, His observed value is 180, which would fall right here on our number line, and his Z score is gonna be 180- the mean. So he's 30 points above the mean, Divided by the standard deviation (180-150)/20=1.5 And then for bill, we're going to do the same thing. His score is also, let's see here his score is 190,(190-160)/15=2And you can probably see just by marking that on the bell curve, that that's actually two standard deviations above the ME, which is more than George is 1.5 standard deviations above the mean. So we can say that Bill is better bowler.

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