Question

jody, a statistics major, grows tomatoes in her spare time. she measures the diameters of each tomato. assume the normal model is appropriate. one tomato was in the 50th percentile. what was its z - score? choose the correct answer below. a. 1 b. 0 c. - 2 d. there is not enough information to complete the problem.

Explanation:

Step1: Recall z - score and percentile relationship

The z - score of a value in a normal distribution represents the number of standard deviations the value is from the mean. The 50th percentile of a normal distribution corresponds to the mean of the distribution.

Step2: Determine z - score for mean

The z - score of the mean in a normal distribution is 0, because the formula for z - score is $z=\frac{x - \mu}{\sigma}$, and when $x = \mu$ (the mean), $z=\frac{\mu-\mu}{\sigma}=0$.

Answer:

B. 0