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

Question

Want to see more full solutions like this?

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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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!

Students have asked these similar questions

Elementary StatisticsBase on the same given data uploaded in module 4, will you conclude that the number of bathroom of houses is a significant factor for house sellprice? I your answer is affirmative, you need to explain how the number of bathroom influences the house price, using a post hoc procedure. (Please treat number of bathrooms as a categorical variable in this analysis)Base on the same given data, conduct an analysis for the variable sellprice to see if sale price is influenced by living area. Summarize your finding including all regular steps (learned in this module) for your method. Also, will you conclude that larger house corresponding to higher price (justify)?Each question need to include a spss or sas output. Instructions: You have to use SAS or SPSS to perform appropriate procedure: ANOVA or Regression based on the project data (provided in the module 4) and research question in the project file. Attach the computer output of all key steps (number) quoted in…

Elementary StatsBase on the given data uploaded in module 4, change the variable sale price into two categories: abovethe mean price or not; and change the living area into two categories: above the median living area ornot ( your two group should have close number of houses in each group). Using the resulting variables,will you conclude that larger house corresponding to higher price?Note: Need computer output, Ho and Ha, P and decision. If p is small, you need to explain what type ofdependency (association) we have using an appropriate pair of percentages. Please include how to use the data in SPSS and interpretation of data.

An environmental research team is studying the daily rainfall (in millimeters) in a region over 100 days. The data is grouped into the following histogram bins: Rainfall Range (mm) Frequency 0-9.9 15 10 19.9 25 20-29.9 30 30-39.9 20 ||40-49.9 10 a) If a random day is selected, what is the probability that the rainfall was at least 20 mm but less than 40 mm? b) Estimate the mean daily rainfall, assuming the rainfall in each bin is uniformly distributed and the midpoint of each bin represents the average rainfall for that range. c) Construct the cumulative frequency distribution and determine the rainfall level below which 75% of the days fall. d) Calculate the estimated variance and standard deviation of the daily rainfall based on the histogram data.

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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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 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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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 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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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 Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (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.