Concept explainers
Let’s eat: A fast-food restaurant chain has 600 outlets in the United States. The following table categorizes them by city population size and location; and presents the number of restaurants in each category. A restaurant is to be chosen at random from the 600 to test market a new menu.
Given that the restaurant is located in a city with a population over 500,000, what is die
Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000?
Given that the restaurant is located in the Southwest what is the probability that it is in a city with a population of 500,000 or less?
Given that the restaurant is located in a city with a population of 500,000 or less, what is the probability that it is in the Southwest?
Given that the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of 50,000 or more?
(a)
The probability that the restaurant is in Northeast, it is given that restaurant is located in a city with a population over 500,000.
Answer to Problem 39E
Explanation of Solution
Given:
The following table categorizes 600 outlets of China restaurant by city population, size, and location.
Population Of City | NE | SE | SW | NW |
Under 50,000 | 30 | 35 | 15 | 5 |
50,000-500,000 | 60 | 90 | 70 | 30 |
Over 500,000 | 150 | 25 | 30 | 60 |
Formula Used:
Probability of an event is given by
For any two dependent events
Where
Calculation:
Let
Let
So,
Therefore,
So, the probability of the event “the restaurant is in Northeast, it is given that restaurant is located in a city with a population over 500,000” is calculated as follows:
Hence, the probability of the event thatthe restaurant is in Northeast, it is given that restaurant is located in a city with a population over 500,000 is
(b)
The probability restaurant is located in a city with a population under 50,000 it is given that the restaurant is located in the Southeast.
Answer to Problem 39E
Explanation of Solution
Given:
The following table categorizes 600 outlets of China restaurant by city population, size, and location.
Population Of City | NE | SE | SW | NW |
Under 50,000 | 30 | 35 | 15 | 5 |
50,000-500,000 | 60 | 90 | 70 | 30 |
Over 500,000 | 150 | 25 | 30 | 60 |
Formula Used:
Probability of an event is given by
For any two dependent events
Where
Calculation:
Let
Let
So,
Therefore,
So, the probability of the event “restaurant is located in a city with a population under 50,000 it is given that the restaurant is located in the Southeast” is calculated as follows:
Hence, the probability restaurant is located in a city with a population under 50,000 it is given that the restaurant is located in the Southeastis
(c)
The probability that the city has a population 500,000 or less, given that restaurant is located in Southwest.
Answer to Problem 39E
The probability that the city has a population 500,000 or less, given that restaurant is located in Southwest is
Explanation of Solution
Given:
The following table categorizes 600 outlets of China restaurant by city population, size, and location.
Population Of City | NE | SE | SW | NW |
Under 50,000 | 30 | 35 | 15 | 5 |
50,000-500,000 | 60 | 90 | 70 | 30 |
Over 500,000 | 150 | 25 | 30 | 60 |
Formula Used:
Probability of an event is given by
For any two dependent events
Where
Calculation:
Let
Let
So,
Therefore,
So, the probability of the event that the city has a population 500,000 or less, given that restaurant is located in Southwest” is calculated as follows:
Hence, the probability that the city has a population 500,000 or less, given that restaurant is located in Southwest is
(d)
The probability that the restaurant is in Southwest, it is given that restaurant is located in a city with a population 500,000 or less.
Answer to Problem 39E
Explanation of Solution
Given:
The following table categorizes 600 outlets of China restaurant by city population, size, and location.
Population Of City | NE | SE | SW | NW |
Under 50,000 | 30 | 35 | 15 | 5 |
50,000-500,000 | 60 | 90 | 70 | 30 |
Over 500,000 | 150 | 25 | 30 | 60 |
Formula Used:
Probability of an event is given by
For any two dependent events
Where
Calculation:
Let
Let
So,
Therefore,
So, the probability of the event “the restaurant is in Southwest, it is given that restaurant is located in a city with a population 500,000 or less” is calculated as follows:
Hence, the probability of the event thatthe restaurant is in Southwest, it is given that restaurant is located in a city with a population 500,000 or less is
(e)
The probability that the city has a population 50,000 or more, given that restaurant is located in South.
Answer to Problem 39E
The probability that the city has a population 50,000 or more, given that restaurant is located in Southis
Explanation of Solution
Given:
The following table categorizes 600 outlets of China restaurant by city population, size, and location.
Population Of City | NE | SE | SW | NW |
Under 50,000 | 30 | 35 | 15 | 5 |
50,000-500,000 | 60 | 90 | 70 | 30 |
Over 500,000 | 150 | 25 | 30 | 60 |
Formula Used:
Probability of an event is given by
For any two dependent events
Where
Calculation:
Let
Let
So,
Therefore,
So, the probability of the event that that “the city has a population 50,000 or more, given that restaurant is located in South” is calculated as follows:
Hence, the probability that that the city has a population 50,000 or more, given that restaurant is located in South is
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Chapter 5 Solutions
Loose Leaf Version For Elementary Statistics
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