Algebra Help!!!

Question

A shipment of beach balls with a mean diameter of 28cm and a standard deviation of 1.3cm is normally distributed. By how many standard deviations does a ball beating with a diameter of 26.7cm differ from mean?

A. 1.3

B. 3

C. 2

D. 1

Answer 1

D. 1

Mean diameter: 

Standard deviation: 

z = (28-27.7)/1.3 = 1

The beach ball is is 1 standard deviation differ from the mean.

Answer 2

What this question is asking for is essentially z-score. A z-score tells you how many standard deviations a piece of data is from the mean of the sample. It's kind of like finding what percent of the standard deviation distance is the data point from the mean. To find the z-score for this problem, we need the difference between the 26.7cm and the 28cm diameter beach balls, which is 28-26.7 = 1.3cm. Next, we divide this difference by the standard deviation to get the number of standard deviations that this beach ball varies by. 1.3cm / 1.3cm = 1, so the number of standard deviations by which a 26.7cm diameter beach ball differs from the mean is (D)1.