CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 7. Sampling Distributions and Estimations

The Central Limit Theorem confirms the intuitive notion that with a large enough number of trials that are performed
on a random variable, the sample means will begin to approximate a normal distribution.

Points to Consider

• What is a binomial experiment?


• What is the difference between a population proportion and a sample proportion?


• How does sample size affect the variation in sample results?

Review Questions

1. The lifetimes of a certain type of calculator battery are normally distributed. The mean lifetime is 400 days
   with a standard deviation of 50 days. For a sample of 6000 new batteries, determine how many batteries will
   last
   a. between 360 and 460 days
   b. more than 320 days
   c. less than 280 days.


2. A sample with a sample size of 40 is taken from a known population whereμ=25 andσ=4 The following
   chart displays the collected data:

24 23 30 17 24 22 23 21 29 25

26 25 29 28 29 29 32 22 27 28

24 32 21 29 30 18 21 24 30 24

25 26 25 27 26 25 27 24 24 25

a. What is the population mean?

b. Determine the sample mean using technology.

c. What is the population standard deviation?

d. Using technology, determine the sample standard deviation.

e. If an infinite number of samples of size 40 were collected from this population, what would be the value

the mean of the sample means?

f. If an infinite number of samples of size 40 were collected from this population, what would be the value

of the standard deviation of the sample means?

Review Answers

1. (a)

z=

x−μ

σ

and z=

x−μ

σ

z=

360 − 400

50

and z=

460 − 400

50

z=− 0. 8 and z= 1. 2