STATS
Introduction to Statistics (MGMT 215)
Hampton University, University College
Test 2: Chapters 4 & 5
Name__________________________________ Date__________________
Instructions: You are required to work the questions independently. Do not seek help from
anyone. Follow Hampton University Code of Conduct.
Fill in the Blank. (1 point each)
A diagram that provides a systematic way of listing all the outcomes in a sample space for a probability experiment consisting of several stages is called ______ _______________.
________________ is the set of all outcomes in the sample space that are not in the event.
The _________________ _________________ _________________ is the method for counting the total number of possible outcomes for a multistage experiment.
A table of listing of the possible outcomes of an experiment and the probability associated with each outcome is called a ___________________ _______________________.
In a discrete probability distribution, the sum of the possible probabilities is always equal to ________.
The expected value of a probability distribution is also called the __________.
How many outcomes are there in a particular binomial trial? ________ .
Under what conditions will the probability of a success change from trial to trial in a binomial experiment? ____________.
In a Poisson experiment, the mean and variance are ___________.
The mean number of work-related accidents per month in manufacturing plant is 1.70. What is the probability there will be no work-related accidents in a particular month? (Assume Poisson distribution) __________ .
Decide whether each statement is true or false. (1 points each)
Each trial in a binomial distribution is independent of the others. (T/F)
In a probability distribution all possible trials are between -1 and 1, inclusive. (T/F)
Conditional probability is used when the two events are independent. (T/F)
For any sample space, the sum of all probabilities is equal to one. (T/F)
The essential difference between a discrete random variable and a discrete probability distribution is that a discrete probability distribution includes the probability. (T/F)
Free Response Section
You Must Show Your Work to Earn Full Credit
Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. What is the probability that an American chosen at random has (10 points)
Traveled to either Canada or Mexico?
Neither traveled to Canada nor Mexico?
Evaluate the expressions. (20 points)
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(a)
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(b) In how many ways can a president, vice president, secretary, and treasurer be elected from a group of 8 people? |
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(c)
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(d) A club with 25 members wants to select a committee of 6 persons. In how many ways can this be done? |
A CPA studied the number of exemptions claimed on tax returns. The data are summarized in the following table. Complete the table and use it to answer the questions below:
(20 points)
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Exemptions, |
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1 |
0.20 |
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2 |
0.50 |
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3 |
0.20 |
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4 |
0.10 |
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Total |
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What is the mean (expected) number of exemptions claimed?
What is the variance and standard deviation of the number of exemptions claimed?
Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution. (15 points)
What is the probability that no automobiles arrive in a particular minute?
What is the probability that no more than one automobiles arrives in a particular minute?
The owner of a pet store is trying to decide whether to discontinue selling clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of customers for a day, and whether they purchase specialty clothes for their pet. The owner had 275 customers that day. (20 points)
What would be the mean and the standard deviation of the number of customers who buy specialty clothes for their pet each day?
What is the probability that exactly 3 of the first 10 customers buy specialty clothes for their pet? Show work.
What is the probability that at least 4 of the first 10 customers buy specialty clothes for their pet? Show work.