Discrete distributions Binomial Poisson Hypergeometric
Continuous distributions Normal We knew and used it to determine
P(X) Using sample data to project to the population inferential
statistics
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Consider the sample mean as a random variable Different values
for sample mean Own mean and s.d. Probability distribution of
sample means Sample distribution of the mean
1. The sampling distribution of the mean will always have the
same mean as the original population. 2. The standard deviation of
the sampling distribution of the mean is referred to as the
standard error of the mean.
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3. If the original population is distributed normally, the
sampling population will also be normal. 4. If the original
population is not normal, the sampling distribution will
approximate normal.
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Given the following probability distribution for an infinite
population with the discrete RV, x: x12 P(x)0.5 Determine the mean
and standard deviation of x. For the sample size n=2, determine the
mean for each simple random sample from the population. For each
sample we just identified, what is the probability this sample will
be selected? Combining the results we just got, describe the
sampling distribution of the mean. Do this again for n=3. What
effect does the change in sample size have on the mean and the
standard error of the mean?
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The average annual hours flown by general aviation aircraft =
130. Assume these hours are normally distributed. Standard
deviation = 30 hours.
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A random variable is normally distributed with = $1500 and =
$100. Determine the standard error of the mean for simple random
samples with the following sample sizes: n=16 n=100 n=400
n=1000
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Airplanes with = 130 and = 30 For a simple random sample of 36
aircraft, what is the probability the average flight time for the
aircraft in the sample was 138 hours?
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A crane is operated by 4 electrical motors working together.
For the crane to work properly, the 4 motors must generate 380 hp.
Each motor produces an average of 100 hp with a standard deviation
of 10 hp. Whats the probability that the crane wont work?
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A store receives a truckload of electric components. Before
accepting shipment, the store will randomly select 9 components for
testing. The shipment will be rejected if the components resistance
is > 300 as listed on their label. The true mean of the
population is 295 , the is 12 , and the population is normally
distributed. What is the probability the load will be
rejected?
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The average length of a hospital stay is 5.7 days. Assuming a
of 2.5 days and a random sample of 50 patients, what is the
probability the average stay for the sample will be 6.5 days? If
the sample had been 8 instead of 50, what further assumption must
we make in order to solve this problem?
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What is the probability that a single, random reading will show
this patient with BP above 150? What is the probability that the
sample mean from 5 readings will show this patient with BP above
150? How many samples must we take before the probability of the
sample mean being less than 150 is.01?
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42.6% of all purchasing agents in the U.S. work force are
women. In a random sample of 200 purchasing agents, 70 are women.
What is the population proportion?What is the sample
proportion?What is the standard error of the sample proportion? If
we took another random sample, whats the probability wed get a
proportion at least as large (.35) as the one we got here?
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Of the 629 imported cars sold in Enterprise last year, 117 were
Toyotas. A random sample of 300 imported cars is conducted. What is
the probability that at least 15% of the vehicles in the sample
will be Toyotas?
