http://www.ck12.org Chapter 5. Normal Distribution
TABLE5.3:(continued)
Number of Sprinkles Deviation Z−scores
223
133
335
322
323
354
194
332
274
233
147
213
262
227
366Figure:A table to be filled in for the sprinkles question.
(c) Create a normal probability plot from your results.
(d) Based on this plot, comment on the normality of the distribution of sprinkle counts on these doughnuts.
Open-ended Investigation: Munchkin Lab.
Teacher Notes: For this activity, obtain two large boxes of Dunkin Donuts’ munchkins. Each box should contain only
one type of munchkin. I have found students prefer the glazed and the chocolate, but the activity can be modified
according to your preference. If you do not have Dunkin Donuts near you, the bakery section of your supermarket
should have boxed donut holes or something similar you can use. You will also need an electronic balance capable
of measuring to the nearest 10thof a gram. Your science teachers will be able to help you out with this if you do
not have one. I have used this activity before introducing the concepts in this chapter. If you remove the words
“z−score”, the normal probability plot and the last two questions, students will be able to investigate and develop an
intuitive understanding for standardized scores and the empirical rule, before defining them. Experience has shown
that this data very closely approximates a normal distribution and students will be able to calculate thez−scores and
verify that their results come very close to the theoretical values of the empirical rule.
Review Answers
- You would expect this situation to vary normally with most students’ hand spans centering around a
particular value and a few students having much larger or much smaller hand spans.
- You would expect this situation to vary normally with most students’ hand spans centering around a
- Most employees could be hourly laborers and drivers and their salaries might be normally distributed,
but the few management and corporate salaries would most likely be much higher, giving a skewed right
distribution. - Many studies have been published detailing the shrinking, but still prevalent income gap between male
and female workers. This distribution would most likely be bi-modal, with each gender distribution by
itself possibly being normal. - You might expect most of the pennies to be this year or last year, fewer still in the previous few years,
and the occasional penny that is even older. The distribution would most likely be skewed left.
1.z≈− 2. 54