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?

Answer 1

Answer:

Zscore = 0.5

Step-by-step explanation:

If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).

By that, we mean that the mean (μ) = 0 and variance ($\sigma^{2}$) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.

Thus:

==> Z score = $\frac{x-\mu}{\sigma}$ = $\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5$