Review Chapter 5 and 6 - Los Angeles Mission College
Math 227 Practice Final
Instructor: Butler Ch. 1-8
1. True/False
a) A 99% confidence interval for [pic] is wider than a 95% confidence interval for [pic].
b) P(A or B) = P(A) + P(B) if event A and event B are mutually exclusive.
c) P(x) can be larger than 1.
d) The mean ([pic]) of the standard normal distribution (Z-table) is 0.
e) The random variable for a binomial distribution is a discrete random variable.
f) As n increases, the margin of error decreases.
g) A binomial distribution is approximately normally distributed if both np and nq are
greater than or equal to 5.
h) As n increases, [pic] increases.
i) If the population distribution is unknown, [pic] is normally distributed for n = 25.
2. Classify the following as nominal-level, ordinal-level, interval-level, or ratio-level measurement.
a) SAT score c) Grade
b) Age d) Nationality
3. If a single card is drawn from an ordinary deck of cards, what is the probability of drawing either a diamond or a 10?
4. A class has fifteen students, six of which are females. If two students are selected at random, one after the other, without replacement, what is the probability that both students are females?
5. If you run a red traffic light at an intersection equipped with a camera monitor, there is a 0.2 probability that you will be given a traffic violation. If you run a red traffic light at this intersection five different times, what is the probability of getting at least one traffic violation?
6. The Board of Trustees at a college has 9 members. Each year, they elect 3 officers (Chairperson, Vice Chairperson, and Secretary). How many different slates of candidates are possible?
7. A group of 2000 randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses.
| |In Favor |Against |No Opinion |
|Male |395 |405 |100 |
|Female |300 |680 |120 |
a) If one person is selected at random from these 2000 adults, find the probability
that this person is in favor of cloning.
b) If one person is selected at random from these 2000 adults, find the probability
that this person is in favor of cloning given the person is a female.
8. In a Maritz poll of adult drivers conducted in July 2002, 45.8% said that they “often” or “sometimes” eat or drink while driving. Assume that this result is true for the current population of all adult drivers. A sample of 18 adult drivers is selected. Let x be the number of drivers in this sample who “often” or “sometimes” eat or drink while driving.
a) Find P(x=10)
b) Find the mean and standard deviation of the probability distribution of x.
9. The following table represents a probability distribution.
|x |0 |1 |2 |3 |
|P(x) |0.15 |0.24 |0.18 |?? |
Find P(x=3).
10. a) State the Central Limit Theorem
b) State four requirements for a binomial experiment.
11. A psychologist has devised a stress test for dental patients sitting in the waiting rooms. According to this test, the stress scores (on a scale of 1 to 10) for patients waiting for root canal treatments are found to be approximately normally distributed with a mean of 7.59 and a standard deviation of 0.73. What percentage of such patients has a stress score
lower than 6.0?
12. To qualify for security officers’ training, recruits are tested for stress tolerance. The scores are normally distributed, with a mean of 62 and a standard deviation of 8. If only the top 20% of recruits are selected, find the cutoff score.
13. The delivery times for all food orders at a fast food restaurant during the lunch hour are normally distributed with a mean of 6.7 minutes and a standard deviation of 2.1 minutes. Find the probability that the mean delivery time ([pic]) for a random sample of 16 such orders at this restaurant is more than 3.0 minutes.
14. The test scores on a 100 point test were recorded for 10 students:
61 93 91 86 55 63 86 82 76 57
a) Identify the five-number summary. (Lowest, [pic], Highest)
b) Find the Mean Median, Mode, and Range.
c) Find the Variance and Standard deviation using the definition.
d) Construct an ordered stem-an-leaf plot.
15. A company randomly selected nine office employees and secretly monitored their computers for one month. The time (in hours) spent by these employees using their computers for non-job-related activities (Playing games, personal communications, etc.) during this month are given here:
7 12 9 8 11 4 14 1 6
a) Use your calculator to find [pic] and [pic].
b) Assume that such times for all employees are normally distributed,
make a 95% confidence interval for the corresponding population mean ([pic]) for all
employees of this company.
16. An auto company wanted to know the percentage of people who prefer to own safer cars even if they have to pay a few thousand dollars more. A random sample of 500 persons showed that 44% of them will not mind paying a few thousand dollars more to have safer cars. Construct a 90% confidence interval for the proportion of all people who will not mind paying a few thousand dollars more to have safer cars.
17. Suppose you wish to estimate a population mean based on a random sample of n observations, and prior experience suggests that [pic]=12.7. If you wish to estimate [pic] correct to within 1.6 with a 95% level of confidence, what should the sample size be?
18. According to the National Association of Colleges and Employers, the entry-level mean salary offered by business consulting firms to college graduates was $43,070 in 2002. A recent random sample of 28 such offers gave [pic] = $45,000 and [pic]=$3200. Use [pic]=0.01; can you conclude that the current mean of such salary offers exceeds $43,070? Assume that all such salary offers are normally distributed.
19. One survey showed that among 785 randomly selected subjects who completed four years of college, 144 smoke. Use [pic]=0.05 to test the claim that the percentage (p) of smoking among those with four years of college is less than the 27% rate for the general population.
20. The given statistics are summarized from paired sample data.
[pic]=5.00, n = 20, and the equation of the regression line is [pic]
a) If [pic], What is the best predicted value of [pic] given that [pic]?
b) If [pic], what is the best predicted value of [pic] given that [pic]?
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