Concept explainers
(a)
To find: the number of people who were surveyed
(a)
Answer to Problem 3CA
There are about 2246 people in the survey.
Explanation of Solution
Given:
Survey Results | |
Cup | 45% |
Cone | 29% |
Sundae | 18% |
Other | 8% |
(margin of error |
Formula Used:
Calculation:
Margin of error =
Squaring both sides,
Thus, there are about 2246 people in the survey.
Conclusion:
There are about 2246 people in the survey.
(b)
To find: reason why the given conclusion is inaccurate to draw from the given data
(b)
Answer to Problem 3CA
More than one-fourth of the adults who were surveyed prefer to have ice-cream in cone.
Explanation of Solution
Given:
“Adults do not prefer to eat their ice cream in cone”
Calculation:
It is inaccurate to draw the conclusion that adults do not prefer to eat their ice cream in cone because from the given data it is clear that more than one-fourth of the adults who were surveyed prefer to have ice-cream in cone.
Conclusion:
More than one-fourth of the adults who were surveyed prefer to have ice-cream in cone.
(c)
To find: the probability that at least three prefer to eat ice cream in a cone
(c)
Answer to Problem 3CA
The probability that at least three prefer to eat ice cream in a cone is
Explanation of Solution
Calculation:
Now, here probability of success is 0.29, since 29% people in survey prefers ice-cream in cone.
Now, to find probability that at least 3 out of 6 people prefer to have ice cream in cone is given by
This is a binomial experiment and for a binomial experiment, the probability of exactly k successes in n trials is given by
Here
Now,
Conclusion:
The probability that at least three prefer to eat ice cream in a cone is
(d)
To find: the reason why the given conclusion is incorrect
(d)
Answer to Problem 3CA
This conclusion might be incorrect as a sample of size 6 is very small and it will have a large margin of error.
Explanation of Solution
Given:
Four of the six people eat ice cream in cone
Calculation:
This conclusion might be incorrect as a sample of size 6 is very small and it will have a large margin of error.
Conclusion:
This conclusion might be incorrect as a sample of size 6 is very small and it will have a large margin of error.
(e)
To find: the margin of error for the survey
(e)
Answer to Problem 3CA
Margin of error is about
Explanation of Solution
Calculation:
Use the formula for margin of error
Margin of error =
Thus, margin of error is about
Conclusion:
Margin of error is about
Chapter 11 Solutions
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