Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The heights of the adult women in a made-up town are mound-shaped, with mean 165 cm and standard deviation 6 cm. Use the 68-95-99.7 idea. About what percentage of the women are between 153 cm and 177 cm? About what percentage are taller than 171 cm? About what percentage are shorter than 147 cm?
A z-score counts standard deviations from the mean and has no units. For mound-shaped data about , and lie within 1, 2 and 3 SDs.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. 153 to 177 cm. These are and . About .
Step 2. Taller than 171 cm. That is . About lie within 1 SD, so lie outside, half of them above: about .
Step 3. Shorter than 147 cm. That is . About lie within 3 SDs, so lie outside, half of them below: about .
Answer: about , and .
Check. These answers lean on the mound shape. For skewed data, the tails would not be equal.
Log in to join the discussion.
Loading…