### 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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Description: ### 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 probab

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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