1) What is the probability that 4 randomly selected people ...
Name: ____________________________
Practice Exam #2
Math 5
Spring 1998
1) What is the probability that 4 randomly selected people all have different birthdays?
2) Choose all that apply. Describe the differences in the Poisson and the binomial
distribution.
a) The Poisson computes probabilities for occurrences of events over some
interval.
b) The Poisson distribution is affected only by the mean, whereas the binomial is
affected by sample size n and probability p.
c) The binomial is discrete and the Poisson is continuous
d) There are no differences
e) The Poisson distribution has discrete values from 1, 2, 3, . . . with no upper
limit. A binomial distribution has discrete values from 1, 2, 3, to n; that is, the
upper limit of values is n.
3) A study of consumer smoking habits includes 156 people in the 18-22 age bracket (58
of whom smoke), 123 in the 23-30 age bracket (37 of whom smoke), and 100 in the
31-40 age bracket (27 of whom smoke).
a) Create a contingency table for the information given.
b) Find the probability of getting someone who is age 23-30 or smokes.
c) Find the probability of getting a smoker that is 23-30.
d) Find the probability of getting someone who is 18-22 or 23-30.
e) Find the probability of getting someone who doesn't smoke and is 31-40
4) Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice
stick. Simultaneously, they take out a single food item and consume it. The possible
pairs of food items that Sally and Sammy consumed are as follows.
chocolate bar - chocolate bar
licorice stick - chocolate bar
banana - banana
chocolate bar - licorice stick
licorice stick - licorice stick
chocolate bar - banana
banana - licorice stick
licorice stick - banana
banana - chocolate bar
a) Find the probability that exactly one licorice stick was eaten.
b) Find the probability that at least one banana was eaten.
5) Determine whether the following is a probability distribution. If not, identify the
requirement that is not satisfied.
|x |P(x) |
|0 |0.191 |
|1 |0.231 |
|2 |-0.014 |
|3 |0.157 |
|4 |0.268 |
|5 |0.167 |
6) Based on meteorological records, the probability that it will snow in a certain town on
January 1st is 0.477. Find the probability that in a given year it will not snow on
January 1st in that town.
7) Determine whether the following is a probability distribution. If not, identify the
requirement that is not satisfied. A police department reports that the probabilities
that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.165, 0.298, 0.268,
0.161, and 0.072 respectively.
8) Of the 51 people who answered "yes" to a question, 14 were male. Of the 98 people
who answered "no" to the question, 6 people were male. Answer the following.
a) Write a contingency table for the data.
b) If one person is selected at random from the group, what is the probability that
the person answered "yes" or was male?
c) What is the probability that a male answered yes?
d) What is the probability that a person was a women and answered no?
9) The probability that a person has immunity to a particular disease is 0.2. Find the mean
number who have immunity in samples of size 17. At what number would you
consider the number people having the disease unusual, and why?
10) Find the probability that 4 randomly selected people all have the same birthday.
Ignore leap years.
11) Use the table of binomial probabilities to find the probability of at least 10 successes if
n = 11 and p = 0.6.
12) The manager of a bank recorded the amount of time each customer spent waiting in
line during peak business hours one Monday. The frequency table below summarizes
the results.
|Waiting Time (minutes) |Number of Customers |
|0-3 |11 |
|4-7 |14 |
|8-11 |9 |
|12-15 |4 |
|16-19 |8 |
|20-23 |3 |
|24-27 |2 |
a) If we randomly select one of the times represented in the table, what is the probability
that it is at least 12 minutes or between 8 and 15 minutes?
b) What is the probability that it is at most 19 minutes?
13) The number of lightning strikes in a year at the top of a particular mountain has a
Poisson distribution with a mean of 2.9. Find the probability that in a randomly
selected year, the number of lightning strikes is 3.
14) What important question must you answer before computing an "and" probability?
How does the answer influence your computation?
15) On an exam on probability concepts, Sue had an answer of -( . Explain how she
knew that this result was incorrect.
16) Do probability distributions measure what did happen or what will probably happen?
How do we use probability distributions to make decisions?
17) A game is said to be "fair" if the expected value for winnings is 0, that is, in the long
run, the player can expect to win 0. Consider the following game. The game costs $1
to play and the winnings (payoff minus your bet) are $5 for red, $3 for blue, $2 for
yellow, and nothing for white. The following probabilities apply. What are your
expected winnings? Does the game favor the player or the owner?
|Outcome |Probability |
|Red |0.02 |
|Blue |0.04 |
|Yellow |0.16 |
|White |0.78 |
18) a) Describe an event whose probability of occurring is 1 and explain what that
probability means.
b) Describe an event whose probability of occurring is 0 and explain what that
probability means.
19) What important question must you answer before computing an "or" probability?
How does the answer influence your computation?
20) A batch consists of 12 defective coils and 88 good ones. Find the probability of
getting two good coils when two coils are randomly selected if the first selection is
replaced before the second is made.
21) A company purchases shipments of machine components and uses this acceptance
sampling plan: Randomly select and test 25 components and accept the whole batch if
there are fewer than 3 defectives. If a particular shipment of thousands of components
actually has a 4% rate of defects, what is the probability that this whole shipment will
be accepted?
22) In a game you roll a fair die and you get $3.00 for a 1 or a 5 and nothing otherwise.
a) Write out the probability distribution.
b) What would you expect to pay to play this game?
c) How much would you expect your earnings to vary from the expected? (Hint:
Find the standard deviation.)
23) The number of calls received by a car towing service averages 9.6 per day (per 24-
hour period). After finding the mean number of calls per hour, find the probability that
in a randomly selected hour the number of calls is 3.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- what is the role of the government
- what is the job of the president
- what is the ethnicity of the us
- what is the probability calculator
- what is the purpose of the eu
- what is half of 3 4 inch
- what is the population of the earth
- what is the purpose of the government
- what is the solution to the equation
- what is the purpose of the president
- what is the etymology of the word
- what is the function of the thyroid