Download The second part of the chapter

The second part of the chapter:
Sample Means

Counts (X) and Proportions (p) describe __________________________

However, we sometimes approximate them with ____________________

Statistics often use ___________________ to describe data
o Examples:

The most common are __________________
Let’s review the difference between population and sample:
Population
Sample
mean
proportion
std. dev
Sample Mean =
Distribution of x:
Distribution of x:
Center:
Center:
Spread:
Spread:
Shape:
Shape:
Recap:
 For one individual obs…

For a sample of observations (of size n)…
Example:
Cola bottles are supposed to be filled with 300mL of soda. However, bottles are
usually normally distributed with an average of 298 mL and a standard deviation
of 3mL.
1- What is the probability of selecting one bottle that is less than 295 mL?
2- What is the probability of selecting a 6-pack that has an average amount
of cola less than 295 mL?
Which question gives you a lower probability?
This means that…
Thus…
However, what if the population isn’t normal?
Central Limit Theorem:
o definition, p. 402
o pictures, p.404
How large of a sample size is needed?

depends…

The more non-normal the population…

General rule:
AP Statistics
5.2- Sample Means Worksheet- A
NAME:______________________
1. An individualized bag of Skittles is claimed to have 2.17 oz. of Skittles in it. The
standard deviation is known to be 0.11 oz. and the weight of Skittles bags is
known to be normally distributed.
a. What is the probability that the weight of one bag of Skittles is less than 2
oz.?
b. If we take a sample of 10 bags, what is the probability that the average
weight of the Skittles bags is less than 2 oz.?
2. The average number of miles that a certain brand of tires lasts (on a standard 4
door sedan) is 65,000 miles with a standard deviation of 1,900 miles. The
mileage of the tires has been shown to follow a normal distribution.
a. What is the probability that one randomly selected tire lasts more than
68,500 miles?
b. What is the probability that the average mileage for all 4 tires on a car is
more than 68,500 miles?
3. Chips Ahoy claims to have 1000 chips in every bag of their cookies. A skeptical
researcher does not believe this. The company claims that the standard deviation
of the chips is 20.5 chips.
a. What is the probability that if the researcher picks one bag to examine, it
will have less than 975 chips?
b. The researcher decides to take a better sample. He selects 45 bags and
examines them. What is the probability that the average number of chips
in these bags is less than 975?
AP Statistics
Section 5.2 – Sampling Distribution of Sample Mean- B
1. Suppose a random sample of 25 observations is selected from a population that is
normally distributed with mean 106 and standard deviation 12.
a. What is the distribution of the sample mean?
b. Find the probability that sample mean exceeds 10.
c. Find the probability that the sample mean will deviate from the population mean
by no more than 4.
d. If the probability that x is less than some unknown value equals .37, find that
unknown value.
2. An important expectation of the recent federal income tax reduction is that consumers
will reap a substantial portion of the tax savings. Suppose estimates of the portion of
total tax saved, based on a random sampling of 35 economists, had a mean of 26%
and a standard deviation of 12%.
a. What is the probability that a sample mean will lie within 1% of the population
mean?
b. 40% of the time, a sample mean of size 35 will be greater than what value?