What are the assumptions for creating a population mean (μ) confidence interval using critical z
values?
FICO scores. Construct a 99% confidence interval for the FICO scores of some loan applicants. A
random sample estimated the mean to be 688, with n=70. Population standard deviation is known
to be 68.
Weight of quarters. How many quarters must be sampled so that a 99% confidence interval has a
margin of error of .025 grams. The standard deviation of quarters is known to be .068 grams.
z  
n    /2 
 E 
2
What are the assumptions for creating a population mean (μ) confidence interval using critical t
values?
Length of time to get a Bachelor’s Degree. A sample of students, size 35, had an estimated mean of
4.8 years taken to earn a Bachelor’s Degree. The sample standard deviation was 2.2 years.
Construct a 95% confidence interval of the population mean.
Pollution levels: The measure of particulate pollution is distributed approximately normal. The
following sample values were taken: 1.7, 1.6, 1.5, 2.0, 2.3, 1.6, 1.6, 1.8, 1.5, 1.7, 2.2, 1.4, 1.6, 1.6,
.09. Construct a 98% confidence interval for the population mean.
Proportions:
What are the conditions necessary to construct a confidence interval for a population proportion?
A survey of 1000 adults found that 29% of those surveyed bought music over the internet. Construct
a 99% confidence interval for the population mean.
Continuing with the previous question. If the music industry wants to conduct another survey, and
they want the margin of error to be ½% point, how many adults will need to be surveyed (still 99%
confidence)?
z 
If there’s an estimate for p̂ : n  pˆ (1  pˆ )   / 2 
 E 
Homework:
Section 8.1, #44, #50
Section 8.2, #30, #36
Section 8.3, #28
2
z 
If not: n  .25  / 2 
 E 
2
Probability Questions:
Fouling Out
The rate of fouls for a college center in the NCAA tournament is 4 per game, where a game
is two halves of 20 minutes per half. A player “fouls out” of a game if they get 5 fouls in a
game.
What is the probability of a center NOT fouling out in a game?
What then is the probability of fouling out?
If a player earns 3 fouls in the first half, the coach will usually sit that player for the rest of
the half. If the player starts the second half, what’s the probability of not fouling out in the
second half? If the coach sits the player for the first 5 minutes of the second half too, what’s
the probability of not fouling out now?
The above makes what assumption about the rate of fouls once a player has four fouls called
on them? Is that reasonable?
Easter Egg Hunt
There’s an Easter Egg Hunt. You’re going to find 3 eggs. Inside the egg is a slip of paper
which awards a prize. The prizes are three categories: chocolate, Peeps, and toys. The
people who created the hunt hid 150 eggs. 80 have Peeps prizes. 45 have chocolate. 25
have toys.
What’s the probability of finding only Peeps?
What’s the probability of finding 2 toys?
What’s the probability of finding 3 toys?
What’s the probability of finding at least 2 toys?
What’s the probability of finding 2 chocolates and 1 toy?
What’s the probability of finding 1 Peep, 1 chocolate, 1 toy?
What’s the probability of finding no toys?
What’s the probability of finding at least 1 toy?