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a.
Check whether the given situation involve Bernoulli trials and explain the reason.
a.
Answer to Problem 1E
No, the given situation does not involve Bernoulli trials.
Explanation of Solution
It is given that 50 dice are rolled to find the distribution of the number of spots on the faces.
The trials are said to be Bernoulli trials under the conditions as follows:
- There are only two possible outcomes, success and failure, on each trial.
- The probability of success, denoted as p, remains the same from trial to trial.
- The trials are independent.
Here, the outcomes of the experiment are, 1,2,3,4,5, and 6. That is, the outcomes of the experiment are more than two. Thus, the first condition for Bernoulli trails is not satisfied and thus, the given situation does not involve Bernoulli trials.
b.
Check whether the given situation involves Bernoulli trials and explain the reason.
b.
Answer to Problem 1E
Yes, the given situation involves Bernoulli trials.
Explanation of Solution
It is given that Type A blood is found in 43% of the population. It is checked how much is it likely that a group of 120 majority may have Type A blood.
Here, the outcomes of the experiment are two, the person has Type A blood and does not have, that is, the first condition for Bernoulli trails is satisfied.
It is given that the Type A blood is found in 43% of the population. Thus, the probability of success remains the same from trial to trial.
Here, the trials are finite and it causes the probabilities to change, making the trials not independent. If the sample selected is less than 10% of the population, it can be stated that the trials are independent.
Here, the sample selected is 120 and it will represent less than 10% of all possible donors.
Thus, the given situation involves Bernoulli trials.
c.
Check whether the given situation involves Bernoulli trials and explain the reason.
c.
Answer to Problem 1E
No, the given situation does not involve Bernoulli trials.
Explanation of Solution
Cards with hearts are selected from a deck of seven cards.
Here, the probability of getting a heart from a deck of 7 cards changes from trial to trial. That is, the second condition for Bernoulli trails is not satisfied.
Thus, the given situation does not involve Bernoulli trials.
d.
Check whether the given situation involves Bernoulli trials and explain the reason.
d.
Answer to Problem 1E
No, the given situation does not involve Bernoulli trials.
Explanation of Solution
A poll of 500 of the likely voters is conducted to see how many favor the proposed budget, to predict the outcome of a vote on the school budget.
Here, the population consists 3,000 and the sample consists of 500 voters, which is more than 10% of the population. That is, the trials are not independent and the third condition for Bernoulli trails is not satisfied.
Thus, the given situation does not involve Bernoulli trials.
e.
Check whether the given situation involves Bernoulli trials and explain the reason.
e.
Explanation of Solution
It was found that about 10% of the packages are not being sealed properly. It is checked whether finding more than 3 are unsealed in 24 packages is likely or not.
The outcomes of the experiment are, the package is sealed properly, and the packages are not sealed properly. Thus, the first condition is satisfied.
It was found that about 10% of the packages are not being sealed properly. That is, the probability of success is 0.10. Thus, the second condition is satisfied.
Here, the trials are finite and it causes the probabilities to change, making the trials not independent. If the sample selected is less than 10% of the population, it can be stated that the trials are independent.
Here, the sample selected is of 24 packages and it will represent less than 10% of all packages.
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Chapter 15 Solutions
Stats: Data and Models
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