Download Basic Statistics

These problems are meant to help you study. The presence of a
problem on this sheet does not imply that there will be a similar
problem on the test. And the absence of a problem from this sheet
does not imply that the test does not have such a problem.
--some probability ideas & probability capabilities …
Be able to draw a two-factor contingency table containing either data counts (from which
probability estimates may be made) or probabilities from the statement of the situation.
Know that joint probabilities are at row-column intersections, that marginal (i.e.,
unconditional) probabilities are the sums of rows and columns, and that the total of these
for all columns or all rows (or all joint cells) equals 1. Use the table to estimate
conditional probabilities or probabilities of unions or ….
Know the definition of conditional probability, P(B|A)=P(A&B)/P(A), and its consequence,
P(A&B) = P(A)*P(B|A).
Independence means that P(B|A)=P(B). This occurs when events don't have an impact on one
another, and should be questioned when there's the possibility that the outcome of one
event does have an impact on the other. A consequence of independence (not
the definition) is that P(A and B) = P(A)*P(B).
Be able to draw a probability tree properly and know that the probabilities in it are
unconditional, then conditional, then (on the "leaves"), joint probabilities.
Be able to use it to solve problems using/involving conditional probabilities.
--2. Suppose a researcher wants to study the exercise habits of college students living in residence halls, by interviewing a
random sample of 120 of these students. What type of sampling design will be used in each of scenario I, II, III, or IV
I. The researcher uses random numbers to select a sample of 120 students from the roster of students living in
dormitories and interviews these students. [[simple random sampling]]
II. The researcher obtains a sample of 120 college students living in dormitories by randomly selecting 30
freshmen, 30 sophomores, 30 juniors, and 30 seniors, and interviews these students. [[stratified random sampling]]
III. The researcher uses the roster of students living in dormitories to select a sample of students
by randomly choosing a resident from among the first 25, and then taking every 25th name on the roster.
[[systematic random sampling]]
IV. The researcher, who happens to be a fulltime student, obtains a sample by asking the students he meets
in his various classes for this semester. [[convenience sampling]]
1. Consider the stem and leaf plot of the times (in minutes) it takes students to get to campus. key/legend: 1 | 0 = 10
1 0 0 3 5 9
2 0 1 2 7
3 0 4 6
Determine the 5-# Summary. [Min = 10, Q1 = 15, Med = 22, Q3 = 36, Max = 42]
4 0 1 2
2. MATCHING
A) Mean B) skewed right C) skewed left D) Median
[2 pts each]
_[A]____a) This measure of center will be the largest if the data is skewed to the right.
_[D]____b) This measure of center is not influenced by outliers.
_[B]____c) The distribution of the ages when people get their drivers license would have this shape.
3. The diameters of 12 tennis balls for two different brands (Wilson and Penn) were measured using a ruler by a group of basic statistics students. The
results are displayed below.
[2 pts each]
Tennis Ball Diameter (mm)
Penn
Wilson
62.5
63.5
64.5
65.5
66.5
[symmetric, mound-shaped] a) What is the shape of the dotplot for the Wilson brand? _____________
[65]
[Penn]
b) Estimate the average diameter of the Wilson brand. ________
c) Which brand shows more variation, Wilson or Penn? ________________
[Right-Tailed]
[4]
d) What is the shape of the dot plot for the Penn brand? _____________________
e) What is the range of the diameters for the Penn Brand? _____
4) Consider the data on the number of registers open at noon at a Kmart over a period of 5 days: 6 8 1 3 2
Find the standard deviation of the number of registers open at noon. Show all work for full credit. [s = 2.915…]
[6]
7) Consider the box-plot below on the time (in minutes) it took selected students to complete an assignment.
[2 pts each]
Give values of the 5 number summary … . [Min = 20, Q1 = 30, Med = 40, Q3 = 55, Max = 70]
8) The work status was recorded for a sample of students and the information is displayed using a Bar Graph.
(refer to the adjoining graph and answer the following questions)
a)
How many students were sampled? __[20]_______
b)
What percent of those sampled are Part-timers (PT)? __[30%]______
c)
What percentage of those sampled is working? __[80%]________
10
8
6
4
2
0
FT
PT
NOT
More Practice Practice Practice Problems …
1. Find the mean, mode, range and standard deviation of: 2, 2, 5, 5, 8, 2
2. Consider the stem and leaf below:
3|245567
4|0023
5|111
6|02
a. Give the 5 number summary.
B. Give the IQR
c. Comment on the shape
3. If P(Rain) = 0.73, P(not rain) = _____
4. If a data set is skewed to the right,
then the median is ____________ (larger, smaller) than the mean.
5. What is the probability of getting a 1 or a 2 if a fair die is rolled? _____
6. What is the probability of getting a 1 and a 2 if a fair die is rolled? _____
7. The (mean, median) is not affected by outliers in a data set.
8. The mean score on a standardized test is 25 with a standard deviation of 5.
What percentage of the data lies from 15 to 35. Assume the data is bell shaped.
9. consider the table by gender and diet program
Weight Watchers
south beach (SB) a) Find P(female)
Male
(M)
15
25
b) Find P (female | weight watchers)
c) Find P (male and South Beach)
Female (F)
30
10
d) Find P(South Beach or female)
e) Are “F” and “WW” independent?
10. One hundred people were asked, Do you favor the death penalty? Of the 33 that answered yes to the
question, 14 were male. Of the 67 that answered no to the question, six were male. If one person is selected at
random, what is the probability that this person answered yes or was a male?
11. If one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack or a queen.
12. If one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack or a heart.
13 . If you toss a fair coin 4 times, what is the probability of getting all heads?
14. A human gene carries a certain disease from the mother to the child with a probability rate of 47%. That is,
there is a 47% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has
four children. Assume that the infections of the four children are independent of one another. Find the
probability that all four of the children get the disease from their mother.
15. A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf
course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to
know how many members regularly use each facility. A survey of the membership indicates that 60% regularly
use the golf course, 42% regularly use the tennis courts, and 9% use neither of these facilities regularly. Given
that a randomly selected member uses the tennis courts regularly, find the probability that they also use the
golf course regularly.
16 A person can order a new car with a choice of 9 possible colors, with or without air conditioning, with or
without heated seats, with or without anti-lock brakes, with or without power windows, and with or without a
CD player. In how many different ways can a new car be ordered in terms of these options?
17 You are taking a multiple-choice test that has 8 questions. Each of the questions has 5 choices, with one correct
choice per question. If you select one of these options per question and leave nothing blank, in how many
ways can you answer the questions?
18 A church has 10 bells in its bell tower. Before each church service 3 bells are rung in sequence. No bell is rung
more than once. How many sequences are there?
19 From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many
different committees are possible?
20 Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and
each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive
first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last.
21 Before going on vacation for a week, you ask your spacey friend to water your ailing plant.
Without water, the plant has a 90 percent chance of dying. Even with proper watering, it has a 20 percent chance of dying.
And the probability that your friend will forget to water it is 30 percent.
(a) What’s the chance that your plant will survive the week?
(b) If it’s dead when you return, what’s the chance that your friend forgot to water it?
(c) If your friend forgot to water it, what’s the chance it’ll be dead when you return?
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 mean = 4 mode = 2 range = 6 stdev = 2.45
2 a) min = 32 Q1 =35 med =40 Q3 =51 max = 62 b) IQR = 16 c) skewed right
3 P(Not Rain) = 0.27
4 smaller
5 1/3
60
7 median
8 95%
9 a) 50% b) 2/3 = 67% c) 31.25% d) 81.25% e) NO P(F) = 50% not equal P(F|W) = 67%
10 39%
11 8/52
12 16/52
13 1/16
14 0.049
15 0.262
16 288
17 390,625
18 720
19 126
20 720, 24, 1/30
21 a = 59% b = 27/41 = 65.85% c = 90%
Notice For # 21
P(No Water) = 0.3
P(Yes Water) = 0.7
P(death | no water) = 0.9
P(live | no water) = 0.1
P(death | water) = 0.2
P(live | water) = 0.8
Now use tree …
Get four cells
P(No water and Death) = 0.3 times 0.9 = 0.27
P(No water and live) = 0.3 times 0.1 = 0.03
P(water and Death) = 0.7 times 0.2 = 0.14
P(water and live) = 0.7 times 0.8 = 0.56
a) P(live) = 0.03 + 0.56 = 0.59
b) P(no water | death) = 0.27/0.41 = 27/41
c) P(death | no water) = 0.9 given in question