Question

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. LetX denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) TableVII in AppendixA. Compare your answer here to that in part (a).

$n=5,p=\frac{3}{5},P(X=4)$

Short answer

Part (a) 0.395.

Part (b) Both answers are the same as 0.395.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

The provided number of trials and success probability for Bernoulli trials is:

$n=5,p=\frac{3}{5},P(X=4)$

Part (a) Step 2. Determine the probabilities by using the binomial probability formula.

Use the formula:

$P\left(X=x\right)=\left(\begin{array}{c}n\\ x\end{array}\right)p^x{\left(1-p\right)}^{n-x}$

We are given $n=5,p=\frac{3}{5},P(X=4)$.

Substitute the given values in the formula,

$$\begin{gathered} P\left(X=5\right)=\left(\begin{array}{c}5\\ 4\end{array}\right){\left(\frac{3}{4}\right)}^4{\left(1-\frac{3}{4}\right)}^{5-4} \\ =0.395 \end{gathered}$$

Part (b) Step 1. Refer to Table VII in Appendix A to find the answer.

After referring to the able VII in Appendix A,the resulted value is 0.395 at the given values $n=5,p=\frac{3}{5},P(X=4)$.

The resulted answers from both the parts are the same 0.395.