Question

A shipment of marbles with a mean diameter of 27 mm and a standard deviation of 0.15 mm is normally distributed. By how many standard deviations does a marble with a diameter of 26.85 mm differ from the mean?

0
0.15
1
2

Answer 1

the answer is 1. there is 1 set of .15mm that separates 27 from 26.85.

Answer 2

A marble of 26.85mm in diameter is 1 standard deviation from the mean.

Explanation:

For an approximately normal distributed random variable, the transformation Z = (X-media) / sd provides the distances from each value of the variable X to the mean measured in standard deviation units. Therefore, if mean = 27mm, sd = 0.15mm, for a marble of 26.85mm in diameter, you have:

Z = (26.85 - 27) / 0.15 = -1.0.

A marble with 26.85mm in diameter is 1 standard deviation from the mean.