The most likely event in a random sample of 100. To determine: The likelihood of the most likely event.

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Answer 1

Question

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

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Answer 2

Question

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

Answer 6

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

Answer 7

Chapter 4, Problem 1UA

To determine

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.

Answer 8

Expert Solution & Answer

Answer to Problem 1UA

The most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The likelihood of the most likely event, “40 people prefer Brand A toothpaste” is 0.0812191.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given info:

The claim of a manufacturer is that, of all the toothpaste buyers, 40% prefer the toothpaste of Brand A.

Justification:

Define the random variable x as the number of toothpaste buyers who prefer the toothpaste of Brand A, in a random sample of 100.

A close inspection of the graph shows that the probability is the highest when number of persons who prefer Brand A is 40, that is, for x=40 . Thus, the most likely event in a random sample of 100 is that 40 people prefer Brand A toothpaste.

The graph reveals that the value of the probability of the event “40 people prefer Brand A toothpaste” is a 0.081.

Calculation:

Here, the claim of the manufacturer is 40% (or 0.40 proportion) of buyers prefer Brand A and preference of each buyer is independent of the other. The size of the random sample (n) is 100. The probability of success (p) is the probability that a buyer prefers Brand A, which is 0.40. Hence, the random variable follows Binomial distribution.

The binomial probability distribution formula is as follows:

P(x)=n!(n−x)!x!pxqn−x .

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Consider n as 100, p as 0.40 and q as 0.60(=1−0.40) and the value of x are 40.

The probability that 40 people prefer Brand A is given below:

Software procedure:

Software procedure for calculating the probability is given below:

Choose Calc > Probability Distributions > Binomial probability distribution.
Choose Probability.
Enter Number of trials as 100 and Event probability as 0.40.
In Input constant, enter the value 40.
Click OK.

Output obtained from MINITAB is given below:

Elementary Statistics: Picturing the World (6th Edition), Chapter 4, Problem 1UA

Thus, the probability that 40 people prefer Brand A is 0.0812191.

Conclusion:

From the graph, it can be seen that the event “40 people prefer Brand A toothpaste” has the highest probability, implying that this is the most likely event. On close inspection of the graph, the likelihood of the event appears to be around 0.081.

From the MINITAB output, the probability that 40 people prefer Brand A toothpaste is 0.0812191.

Answer 12

Ch. 4.1 - Prob. 1TY Ch. 4.1 - Prob. 2TY Ch. 4.1 - Prob. 3TY Ch. 4.1 - Prob. 4TY Ch. 4.1 - Prob. 5TY Ch. 4.1 - Prob. 6TY Ch. 4.1 - Prob. 7TY Ch. 4.1 - What is a random variable? Give an example of a...Ch. 4.1 - What is a discrete probability distribution? What...Ch. 4.1 - Is the expected value of the probability...

The most likely event in a random sample of 100. To determine: The likelihood of the most likely event.

The most likely event in a random sample of 100. To determine: The likelihood of the most likely event.

Answer to Problem 1UA

Explanation of Solution

Want to see more full solutions like this?

Chapter 4 Solutions

The most likely event in a random sample of 100.

To determine: The likelihood of the most likely event.