1. Section 9.4: Normal Distributions

2. Objective(s):
By following instructions, students will be able to:
Use characteristics of a normal distribution to make estimates and probability predictions about the population that the data represents.

3. Def: A bell shaped symmetric distribution with a tail on each end is called a normal distribution.

4. Explore
Use a graphing calculator and the infant birth mass data in the table below to determine if the
set represents a normal distribution.

5. Explore B

6. explain 2A

7. explain 2B
Sketch a relative frequency histogram. The heights of the bars now indicate relative frequencies.

8. explain 2C
Recall from the first Explore that the mean of this data set is 3.5 and the standard deviation
is By how many standard deviations does a birth mass of 3.2 kg differ from the mean?
Round to one decimal place. Justify your answer.

11. explain 1A The masses (in grams) of pennies minted in the United
States after 1982 are normally distributed with a mean of
2.50 g and a standard deviation of 0.02 g.
explain 1A
Find the percent of these pennies that have a mass between
2.46 g and 2.54 g.

12. explain 1B The masses (in grams) of pennies minted in the United
States after 1982 are normally distributed with a mean of
2.50 g and a standard deviation of 0.02 g.
explain 1B
Find the percent of these pennies that have a mass between
2.48 g and 2.52 g.

13. Your-Turn #1
Find the percent of these pennies that have a mass between 2.44 g and 2.56 g.

14. explain 2A
The masses (in grams) of pennies minted in the United States after 1982 are normally distributed with a mean of 2.50 g and a standard deviation of 0.02 g.
Estimate the probability that a randomly chosen penny has a mass greater than 2.52 g.

15. explain 2B
The masses (in grams) of pennies minted in the United States after 1982 are normally distributed with a mean of 2.50 g and a standard deviation of 0.02 g.
Estimate the probability that a randomly chosen penny has a mass greater than 2.56 g.

16. Your-Turn #2
Find the probability that a randomly chosen penny has a mass less than 2.54 g.

17. HW:
Sec 9.4 #s 1-17 ALL