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Number of Students:
Transfer Program
CTE (Voc Ed) Program
Lifelong-Learning
Age:
25 or under
532
45
51
Over
25
108
392
177
a) What’s the probability of being a Transfer student or a CTE student?
b) What’s the probability of being a Transfer student and a CTE student?
c) What’s the probability of being a Lifelong-Learner and young?
d) What’s the probability of being a Lifelong-Learner or young?
e) What’s the probability of being a Transfer Student given that you’re old?
2) Historically, players for a particular school have made 3,192 out 3,988 free throws. A team will
attempt 20 free throws in a game.
a) What is the probability of making at least 70% of their free throws?
b) What is the probability of missing more than 50% of their free throws?
c) What’s the probability of making the last two free throws?
d) What is the probability of making all the free throws?
e) What is the mean and standard deviation of how many free throws will be made?
3) A company has begun making nano-tubes. The average rate of flaws in the tubes is 1 flaw in
every 2 millimeters.
a) What is the probability of making 1 millimeter tube without a flaw?
b) What is the probability of a 3 millimeter tube having more than 2 flaws?
c) What’s the probability of at least 1 flaw in 1.5 millimeter tube?
d) What is the mean and standard deviation of 1 millimeter tube?
4) Collecting stamps. A stamp collector buys old used stamps from estate sales of stamp collectors.
The probability distribution of the population of stamps and their values is:
Value:
$0
$0.10 $0.25 $0.50 $1
$3
$5
$10
$20
$50
Probability .12
.29
.26
.11
.08
.07
.04
.01
.01
.01
a) Of a stamp chosen at random at an estate sale, what is the expected value and standard
deviation of the stamp?
b) What is the probability of a stamp being worth more than $1?
A study is done to discover the average amount of money that households donate to non-profits.
Assumption: distribution of donations is normal OR our sample size is >30 so the distribution of the
mean is approximately normal.
After surveying 20 households, a sample mean of $732 was found. The population standard
deviation is known to be $120.
Construct a 95% confidence interval for the mean donation.
What’s the standard error for the sample mean?
What’s the critical zα/2 for a 95% confidence interval?
What’s the margin of error for a 95% confidence interval?
We would like to have a margin of error be +/- of $100 (at 95% confidence). How many household
would need to be sampled to have a margin of error be $100?
z  
n    /2 
 m 
2
--------------------------Problem is same as above, but population standard deviation is not known
Assumption: distribution of donations is normal OR our sample size is >30 so the distribution of the
mean is approximately normal.
After surveying 20 households, a sample mean of $732 was found. The standard deviation of the
sample is $120
Since we don’t have the population standard deviation and must use a sample, we will not use a
normal distribution and z-scores. Instead we will use which distribution?
Construct a 95% confidence interval for the mean donation.
How many degrees of freedom are there?
What’s the estimated standard error for the sample mean?
Argument for the inverted t-distribution is invT(area in one tail, degrees freedom)
What’s the critical tα/2 for a 95% confidence interval?
What’s the margin of error for a 95% confidence interval?
Note: when sample size gets large (>30), the t-distribution becomes very close to the normal
distribution, and some people will just switch to normal for critical values. However, one should
still refer to the distribution as a t-distribution if the population standard deviation is not known.