Question

A shipment of racquetballs with a mean diameter of 60 mm and a standard deviation of 0.9 mm is normally distributed. By how many standard deviations does a racquetball with a diameter of 58.2 mm differ from the mean?

0.9
1
2
3

Answer 1

Put another way, what's the absolute difference between \(58.2\) and the mean \(60\)? How many standard deviations is this?

Answer 2

1.8 so would it be B?

Answer 3

Not quite. \(1.8\text{ mm}\) is just the difference between this point and the mean.

We want to know how many standard deviations away from the mean this is. This basically comes down to a sort of unit conversion. One standard deviation is \(0.9\text{ mm}\), so two standard deviations is \(2\times0.9=1.9\text{ mm}\). So the answer would be C.

Answer 4

Oh okay, that makes sense. Thank you so much!

Answer 5

yw