**Tutorial Exercise**Consider a binomial random variable with \( n = 9 \) and \( p = 0.7 \). Let \( x \) be the number of successes in the sample. Evaluate the probability.\[ P(3 \leq x \leq 6) \]**Step 1**A binomial experiment consists of \( n \) identical trials with probability of success \( p \) on each trial. The table of cumulative binomial probabilities gives probability values of \( P(x \leq k) \) for the random variable \( x \) with \( k \) successes. The graph of the binomial distribution for \( n = 9 \) and \( p = 0.7 \) is below.**Graph:**- The graph is a histogram illustrating the binomial distribution of the probabilities of \( x \), the number of successes. - The x-axis represents the number of successes ranging from 0 to 9.- The y-axis represents the probability \( P(x) \) of observing exactly \( x \) successes.- The bars indicate the probability mass function of the binomial distribution for each \( x \).**Explanation:**Of interest is \( P(3 \leq x \leq 6) \), which is represented by the bars \( x = 3, 4, 5, 6 \). The table will give the cumulative probability \( P(x \leq 6) \) by summing the areas for the bars \( x = 0, 1, 2, 3, 4, 5, \) and \( 6 \). Since we do not need the area for \( x = 0, 1, 2 \), we can subtract the area for these bars from the area for all seven bars. Thus, the needed probability can be found using \( P(x \leq 6) - P(x \leq 2) \).

The given data is as follows:Sample size, Probability of success,

Answered: Tutorial Exercise Consider a binomial…

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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