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Practice Problems for Exam 2
- The weight in grams of Canadian goose eggs is approximately normally
distributed with mean 280 grams and standard deviation 17 grams.
- Convert the interval involving x into an interval involving z:
250 < x < 290
- Convert the interval involving z into an interval involving x:
z < -2.51
- The number of accidents every 20 minutes during the morning commute in
the Los Angeles Freeways is shown in the following table. Construct a
control chart and list any out of control signals. Then interpret your
findings.
| Time |
6:00 |
6:20 |
6:40 |
7:00 |
7:20 |
7:40 |
8:00 |
8:20 |
8:40 |
9:00 |
9:20 |
9:40 |
| # Accidents |
2 |
5 |
3 |
4 |
8 |
3 |
12 |
2 |
4 |
3 |
3 |
2 |
- The number of students per class at LTCC is approximately Normally
distributed with a mean of 18 and a standard deviation of 5.
- Find the probability that a class selected at random will have
between 16 and 25 students.
- Find the probability that 10 randomly selected classes will have a
mean that is less than 20 students.
- In reaction to the budget cuts LTCC will be cancelling all classes
in the bottom 10th percentile. At least how many
students must a class have in order to not get cancelled?
- Twenty percent of all customers at Tahoe Burger Pit order a double
burger. If 45 randomly selected customers are observed what is the
probability that at least 10 of them will order a double burger?
Comment on whether it is appropriate to use the normal distribution for your
calculations.
- The pass rate for statistics students at the California Community
College system is 68%. If 34 statistics students are randomly
selected, what is the probability that fewer than 60% will pass?
Comment on whether it is appropriate to use the normal distribution for your
calculations.
- Biologists are studying the nesting locations of the endangered spotted
werpler to see whether the bird has a preference near or close to the ocean.
For each number of miles from the ocean, they scoured 50 acres and counted
how many of these acres contain a nesting site. The table below shows
the findings. List any out of control signals and interpret your
findings.
| Ocean Dist |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Nests |
0 |
2 |
6 |
3 |
4 |
2 |
5 |
3 |
4 |
12 |
3 |
| Prop: Nests/50 |
0 |
.04 |
.12 |
.06 |
.08 |
.02 |
.1 |
.06 |
.08 |
.24 |
.06 |
- You want to estimate the proportion of college students who were not
able to purchase all of their textbooks this quarter by the first week of
classes due to financial difficulties. If you want to construct a 90
percent confidence interval and have an error of no more than plus or minus
4%, how many college students should you survey?
- A study was done to estimate the average time it takes for an LTCC
student to walk from their car to their classroom. The 38 randomly
selected students averaged 162 seconds and their standard deviation was 34
seconds.
- Construct the appropriate 95% confidence.
- Use a complete sentence to interpret this interval.
- The 95% represents a probability. Use a complete sentence to
state what this probability means.
- Comment on whether it was appropriate to use the normal distribution
for this analysis.
- A study was done to estimate the proportion of Americans who think that
it is a good idea for the Government to come up with a federal public health
care option. Of the 250 randomly selected Americans surveyed, 95
responded that it is a good idea.
- Construct the appropriate 95% confidence interval.
- Use a complete sentence to interpret this interval.
- The 95% represents a probability. Use a complete sentence to
state what this probability means.
- Comment on whether it was appropriate to use the normal distribution
for this analysis.
- A recent control study was done to see if taking a nap makes people
smarter. The researcher gave an IQ test to 53 people from the control
group who did not take a nap and 41 from the treatment group who did take a
nap. The control group averaged 74% on the test and had a standard
deviation of 9%. The treatment group averaged 82% and had a standard
deviation of 15%.
- Construct the appropriate 95% confidence interval.
- Use a complete sentence to interpret this interval.
- The 95% represents a probability. Use a complete sentence to
state what this probability means.
- Comment on whether it was appropriate to use the normal distribution
for this analysis.
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