7.3 Normal Sampling and Modelling


This lesson is about applying a Normal Distribution to data sets and discrete data.


Ex 1 The table shows the past 20 years of a mutual fund. The data is assumed to be normally distributed. (p. 432)

Year

Return (%)

(a) What do we need in order to discuss this as a normal distribution?


(b) What is the probability that the annual return will be

(i) at least 9%?

(ii) negative?


(c) Out of the next ten years, how many years should we expect a return greater than 6%?

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

7.2

12.3

17.1

17.9

10.8

19.3

12.2

-13.1

20.2

18.6

6.4

27.0

14.5

25.2

-0.5

2.4

16.7

12.8

2.9

18.8


Ex 2 A chocolate company produces boxes of chocolate. The number of pieces in each box is assumed to be normally distributed with a mean of 48 pieces and a standard deviation of 4.3 pieces. The boxes must have between 44 and 55 pieces in order to not rip off the customer or cost the company too much.


(a) What kind of data is this?


(b) What is the probability that a random box contains exactly 50 pieces?


(c) The company produces 130 000 boxes per shift. What percentage will be rejected?


p. 439# 1-3, 8-9