Download Probability Sampling Distribution

Practice Final
1. __________ display how a total is dispersed into several categories. This
graph is very appropriate for qualitative data, or any data where percentage
of occurrence makes sense.
2. __________ retain the original values in a data set.
3. __________ identify the frequency of events or categories in decreasing order
of frequency of occurrence.
4. __________ display how data change over time. It is best if the units of time
are consistent in a given plot.
5. __________ are useful for quantitative or qualitative data. With
qualitative data, the frequency or percentage of occurrence can be
displayed. With quantitative data, the measurement itself can be
displayed
5. __________
6. A survey of 300 teenagers was taken to see which sport was their favorite to
watch on television. The circle graph below displays the results. How
many teenagers are watching each of the sports?
7. Below is a histogram displaying the test scores for students in a statistics class. Categorize the distribution shape
A)
8. A sample of 12 children was taken from a daycare. A
dotplot of the average number of hours of daily
television viewing is shown here. How many children
watch television less than 1 hour per day?
B)
9.Following is a list of prices (to the nearest dollar) for college textbooks.
Make a stem-and-leaf display for these data.
33
27
2
26
34
6
17
29
28
25
35
20
18
47
41
51
10. The durations of 14 commercials are below (in seconds).
Find the mean, median, and mode of these durations.
40
40
10
10
40
65
40
60
40
40
45 120
65
40
11. A random sample of 9 walleyed pike from Salty Lake had the following
weights (rounded to the nearest pound).
4
6
12
3
5
9 10
2
4
A. Find the range.
B. Find the sample mean.
12. Create a 5 number summary and box-and-whisker plot
3
4
11
6
5
7
6
2
4
13. A professor records the percentage of student who score in a certain grade range on a test. Estimate the average score for
the test.
Score
59-60 61-70 71-80 81-90 91-100
Percent of Grade
15%
10%
20%
30%
25%
14. Luke took a test and scored in the 74th percentile. What percentage of the
scores were above his score?
A graduate school committee is studying the relationship between x = undergraduate grade
point average (GPA) and y = the score on the Graduate Record Exam (GRE) for a random
sample of applicants. (#15-18)
x (GPA)
3.2
3.9
4.0
3.4
3.7
3.0
y (GRE)
725
788
775
647
800
672
15. Based on a scatter diagram, what would you estimate the linear correlation coefficient
to be? (Positive 1, Negative 1, Close to 0?)
16. Compute the sample correlation coefficient (r2).
17. What is the equation for the least squares line?
18. If a student has a grade point average of 3.5, what does the least-squares line
predict for the score on the Graduate Record Exam?
19. A random sample of 500 new hybrid vehicles showed that 150 required repairs
within the first warranty year.
A. What is the probability that a new hybrid vehicle will NOT need repairs within the
first warranty year?
B. What is the probability that a new hybrid vehicle WILL need repairs within
the first warranty year?
20. If you roll a single fair die and count the number of dots on top, what is the
probability of getting a number less than 4 or a 5 on a single throw?
Use this info to
help you with your
calculations:
∑x =21.2
∑y = 4407
∑x2 =75.7
∑y2 =3,257,387
∑xy =15,669
21. You roll two fair dice, a white one and a green one.
A. Find P(a number greater than 3 on the white die and exactly 2 on the green die).
B. Find P(exactly 4 on the white die and an even number on the green die).
C. Find P(exactly 4 on the white die and exactly 4 on the green die).
22. An urn contains 8 marbles identical in every aspect except color. There is 1 red marble,
2 green marbles, and 5 blue marbles.
A. You draw two marbles from the urn, but replace the first marble before drawing the
second. Find the probability that the first marble is green and the second is red.
B. Repeat part A, but do not replace the first marble before drawing the second.
23. The basketball coach found that 11% of the basketball players have an A average
in school. If 2% of the students at the school are basketball players, what is the
probability that a student chosen at random will be a basketball player with an A
average?
24. A hospital administration completed a survey of patients regarding satisfaction with care
and type of surgery. The results follow:
Heart Hip Knee Total
Not Satisfied
7
12
2
21
Neutral
15
38
10
63
Satisfied
32
16
25
73
4
22
23
49
58
88
60
206
Very Satisfied
Total
Assume the table represents the entire population of patients. Find the probability
that a patient selected at random is
A. Neutral
B. Very satisfied and had hip surgery
C. Neutral, given that they had knee surgery
D. A heart surgery patient
E. Very satisfied, given that they had hip surgery
F. Satisfied and had heart surgery
25. George has 5 ties, 6 shirts, and 3 pairs of pants. How many different outfits
can he wear if he chooses one tie, one shirt, and one pair of pants for each outfit?
26. In how many ways can 10 athletes be awarded a first-place medal, a secondplace medal, and a third-place medal?
27. In how many different ways can a student choose 5 out of 10 problems to complete
on a take-home exam?
28. The following data are based on a survey taken by a consumer research firm.
In this table x = number of televisions in household and % = percentages of
U.S. households.
5 or more
x
0
1
2
3
4
% 5% 10% 30% 35% 12%
8%
A. What is the probability that a household selected at random has less than
3 televisions?
B. What is the probability that a household selected at random has more than
4 televisions?
C. Compute the expected value of the x distribution (round televisions of 5 or
more to 5).
D. Compute the standard deviation of the x distribution (round televisions of 5
or more to 5).
29. A meteorologist found from the past year’s records that it rained 21% of the days.
Based on this information, what is the probability that for a random sample of 18
days, it rained 4 of those days?
30. Of those people who lose weight on a diet, 90% gain all the weight back. In a
random sample of 12 dieters who have lost weight, what is the probability of
each of the following?
A. All 12 gain the weight back.
B.
9 gain the weight back.
C. 8 gain the weight back.
D. From 8 to 10 gain the weight back, including 8 and 10.
31. The manager of a supermarket found that 72% of the shoppers who taste a free
sample of a food item will buy the item. What is the expected number of shoppers
that will buy the item if a random sample of 50 shoppers taste a free sample?
32. The probability that merchandise stolen from a store will be recovered is 15%.
Suppose a random sample of 8 stores, from which merchandise has been stolen,
is chosen find the mean  and standard deviation σ of this probability distribution.
33. Draw a normal curve.
34. According to the empirical rule, for a distribution that is symmetrical and bell-shaped
approximately what % of the data values will lie
A) within one standard deviation on each side of the mean.
B) within two standard deviations on each side of the mean.
C) within three standard deviations on each side of the mean.
35. According to the empirical rule, the delivery time for a package sent within the United States is normally distributed with
mean of 4 days and standard deviation of approximately 1 day. If 300 packages are being sent, how many packages to we
expect to arrive in less than 3 days?
36. Maria and Zoe are taking Biology 105, but are in different classes. Maria’s
class has an average of 75% with a standard deviation of 6% on the midterm
while Zoe’s class has an average of 85% with a standard deviation of 10%.
Assume that scores in both classes follow a normal distribution.
A. Convert Maria’s midterm score of 86 to a standard z score.
B. Convert Zoe’s midterm score of 92 to a standard z score.
C. Who do you think did better relative to their class?
37. The lifetime of a SuperTough AAA battery is normally distributed with
mean  = 38.5 hours and standard deviation  = 6.3 hours. For a battery
selected at random, what is the probability that the lifetime will be
A. 29 hours or less?
B. 34 hours or more?
38. Complete the following definitions
A. A __________ is a subset of measurements from the population.
B. A __________ can be thought of as a set of measurements (or counts), either
existing or conceptual.
C. A __________ is a numerical descriptive measure of a population.
Word Bank #38
Population
Sample
Parameter
Statistic
Estimate
Probability Sampling Distribution
D. A __________ is a numerical descriptive measure of a sample.
39. The weights of envelopes sent from an insurance office are normally distributed with mean  = 15 ounces and standard
deviation  = 2.5 ounces. The mail room clerk would like to know the average weight of 20 envelopes. What is the
probability that the mean weight x is
A. heavier than 13 ounces?
B. lighter than 11 ounces?
40. The manufacturer of a coffee dispensing machine claims the ounces per cup is mound shaped and symmetrical with mean
 = 7 ounces and standard deviation  = 0.8 ounce. If 40 cups of coffee are measured, what is the probability that the
average ounces per cup x is
A. less than 6.8 ounces?
B. more than 7.4 ounces?
C. between 6.8 and 7.4 ounces?
41.Latasha is a waitress at Seventh Heaven Hamburgers. She wants to estimate the mean amount each group at a table leaves
for a tip. A random sample of 42 tables had a mean of x = $7.30. Based on long term experience,  ≈ $2.92.
A. Find a 90% confidence interval for the average amount left by all groups.
B. Use part A to estimate an interval of dollar values for Latasha’s total tips for a shift with 42 tables.
42. How healthy are the employees at Direct Marketing Industry? A random sample of 12 employees was taken and the
number of days each was absent for sickness was recorded (during a one-year period). Use these data to create a 95%
confidence interval for the population mean days absent for sickness. x  5.08 s  3.48
2
6
5
8
3
5
7
11
10
3
0
1
43. A random sample of 90 shoppers were interviewed and 50 said they prefer to shop alone rather than with someone else.
A. Let p represent the proportion of all shoppers at this mall who would prefer to
shop alone. Find a point estimate p̂ for p.
B. Find a 90% confidence interval for p.
44. A machine in the lodge at a ski resort dispenses a hot chocolate drink. The average cup of hot chocolate is supposed to
contain 7.75 ounces. We may assume that x has a normal distribution with  = 0.3 ounces. A random sample of 16 cups
of hot chocolate from this machine had a mean content of 7.62 ounces. Do you think the machine needs an adjustment?
Use a 5% level of significance and test whether the mean amount of liquid is different than 7.75 ounces.
A. State the null and alternate hypotheses.
B. Compute the value of the test statistic.
C. Find the P-value for the sample test statistic.
D. Based on your answers for parts AD, what is your conclusion?
45. The average number of miles on vehicles traded in at Smith Brothers Motors is 64,000. Smith Brothers Motors has started
a new deal offering lower financing charges. They are interested in whether the average mileage on trade-in vehicles has
decreased. Test using  = 0.01 and the data from a random sample of trade in vehicles. Assume mileage is normally
s  27,800
distributed. The mileages are in thousands. x  62, 400
A. State the null and alternate hypotheses.
39
90
47
50
62
99
110
41
58
28
B. Compute the value of the test statistic.
C. Find the interval containing the P-value for the sample test statistic.
D. Based on your answers for parts AD, what is your conclusion?
46. Results from a previous study showed 79% of all high school seniors from a certain city plan to attend college after
graduation. In a random sample of 200 high school seniors from this city, 162 planned to attend college. Does this
indicate that the percentage has increased from that in the previous study? Test at 5% level of significance.
A. State the null and alternate hypotheses.
B. Compute the value of the test statistic.
C. Find the P-value for the sample test statistic.
D. Based on your answers for parts AD, what is your conclusion?