### Binomial Distribution Probability CalculationAssume that a procedure yields a binomial distribution with a trial repeated $ n = 14 $ times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of $ k = 4 $ successes given the probability $ q = 0.79 $ of success on a single trial.**(Report answer accurate to 4 decimal places.)**\[ P(X = k) = \][Enter an integer or decimal number]### Explanation of Steps:1. **Understanding the Problem:** - We have a binomial distribution scenario. - Number of trials ($ n $): 14 - Number of successes ($ k $): 4 - Probability of success on a single trial ($ p $): 0.792. **Using the Binomial Probability Formula:** The probability $ P(X = k) $ for a binomial distribution can be calculated using the formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Where: - $\binom{n}{k}$ is the combination of n trials taken k at a time. - $ p^k $ is the probability of success raised to the power of the number of successes. - $ (1-p)^{n-k} $ is the probability of failure raised to the power of the number of failures. 3. **Calculation:** You can use a calculator, Excel, StatDisk, or any other technological tool to plug in the values and compute the probability.### Detailed Steps for Using Excel:1. Open Excel and click on a cell where you want to display the result.2. Use the built-in function `BINOM.DIST(x, n, p, FALSE)`: - `x` = number of successes (k in this context, which is 4) - `n` = number of trials (14) - `p` = probability of success (0.79) - `FALSE` indicates it is for the exact probability, not cumulative. So the formula will be: \[ \text{=BINOM.DIST(4, 14, 0.79, FALSE)} \]3. Press Enter to

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Binomial distribution: The probability mass function (pmf) of a binomial random variable X is given…

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Assume that a procedure yields a binomial distribution with a trial repeated n = 14 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k = 4 successes given the probability q= 0.79 of success on a single trial. %3D

Assume that a procedure yields a binomial distribution with a trial repeated n = 14 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k = 4 successes given the probability q= 0.79 of success on a single trial. %3D

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

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.

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Question

### Binomial Distribution Probability Calculation

Assume that a procedure yields a binomial distribution with a trial repeated $ n = 14 $ times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of $ k = 4 $ successes given the probability $ q = 0.79 $ of success on a single trial.

**(Report answer accurate to 4 decimal places.)**

\[ P(X = k) = \]
[Enter an integer or decimal number]

### Explanation of Steps:

1. **Understanding the Problem:**
- We have a binomial distribution scenario.
- Number of trials ($ n $): 14
- Number of successes ($ k $): 4
- Probability of success on a single trial ($ p $): 0.79

2. **Using the Binomial Probability Formula:**
The probability $ P(X = k) $ for a binomial distribution can be calculated using the formula:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Where:
- $\binom{n}{k}$ is the combination of n trials taken k at a time.
- $ p^k $ is the probability of success raised to the power of the number of successes.
- $ (1-p)^{n-k} $ is the probability of failure raised to the power of the number of failures.

3. **Calculation:**
You can use a calculator, Excel, StatDisk, or any other technological tool to plug in the values and compute the probability.

### Detailed Steps for Using Excel:
1. Open Excel and click on a cell where you want to display the result.
2. Use the built-in function `BINOM.DIST(x, n, p, FALSE)`:
- `x` = number of successes (k in this context, which is 4)
- `n` = number of trials (14)
- `p` = probability of success (0.79)
- `FALSE` indicates it is for the exact probability, not cumulative.

So the formula will be:
\[ \text{=BINOM.DIST(4, 14, 0.79, FALSE)} \]
3. Press Enter to

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