Suppose that you and two friends go to a restaurant, which last month filled approximately 90.5% of the orders correctly. Can you please complete part (d) below. a.What is the probability that all three orders will be filled correctly? b. What is the probability that none of the three orders will be filled correctly? c. What is the probability that at least two of the three will be filled correctly? d. What are the mean and standard deviation of the binomial distribution used in (a) through (c)? Interpret these values.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Question:
Suppose that you and two friends go to a restaurant, which last month filled approximately 90.5% of the orders correctly. Can you please complete part (d) below.
a.What is the probability that all three orders will be filled correctly?
b. What is the probability that none of the three orders will be filled correctly?
c. What is the probability that at least two of the three will be filled correctly?
d. What are the mean and standard deviation of the binomial distribution used in (a) through (c)? Interpret these values.
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Obtain the probability that all three orders will be filled correctly.
The probability that all three orders will be filled correctly is obtained below:
Use Excel to obtain the probability value for x equals 3.
Follow the instruction to obtain the P-value:
- Open EXCEL
- Go to Formula bar.
- In formula bar enter the
function as“=BINOMDIST” - Enter the number of success as 3.
- Enter the Trails as 3.
- Enter the probability as 0.905.
- Enter the cumulative as False.
- Click enter.
EXCEL output:
From the Excel output, the P-value is 0.7412.
Thus, the probability that all three orders will be filled correctly is 0.7412.
Obtain the probability that none of the all three orders will be filled correctly.
The probability that none of the all three orders will be filled correctly is obtained below:
Use Excel to obtain the probability value for x equals 0.
Follow the instruction to obtain the P-value:
- Open EXCEL
- Go to Formula bar.
- In formula bar enter the function as“=BINOMDIST”
- Enter the number of success as 0.
- Enter the Trails as 3.
- Enter the probability as 0.905.
- Enter the cumulative as False.
- Click enter.
EXCEL output:
From the Excel output, the P-value is 0.0009.
Thus, the probability that none of the all three orders will be filled correctly is 0.0009.
Obtain the probability that at least two of the three will be filled correctly.
The probability that at least two of the three will be filled correctly is obtained below:
Use Excel to obtain the probability value for x equals 1.
Follow the instruction to obtain the P-value:
- Open EXCEL
- Go to Formula bar.
- In formula bar enter the function as“=BINOMDIST”
- Enter the number of success as 1.
- Enter the Trails as 3.
- Enter the probability as 0.905.
- Enter the cumulative as True.
- Click enter.
EXCEL output:
From the Excel output, the P-value is 0.0254.
Thus, the probability that at least two of the three will be filled correctly is 0.9746
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