Use n=6 and p = 0.7 to complete parts (a) through (d) below. (a) Construct a binomial probability distribution with the given parameters. P(x) 0 1 2 3 4 5 6 (Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random variable using Hx= [x P(x)] and 6x = √[x² • P(x)]- µ² Hx = (Round to two decimal places as needed.) σx = (Round to two decimal places as needed.) Hx= x = ■ (c) Compute the mean and standard deviation, using μx = np and ox=√/np(1-p). (Round to two decimal places as needed.) (Round to two decimal places as needed.) || (d) Draw a graph of the probability distribution and comment on its shape. Which graph below shows the probability distribution? OA. 0.5- AP(x) 0.25- Q The binomial probability distribution is ▼ OB. APX) 0.5 0.25- Q O C. APX) 0.5- 0.25- Q O D. 0.5 APX) 0.25-1
Use n=6 and p = 0.7 to complete parts (a) through (d) below. (a) Construct a binomial probability distribution with the given parameters. P(x) 0 1 2 3 4 5 6 (Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random variable using Hx= [x P(x)] and 6x = √[x² • P(x)]- µ² Hx = (Round to two decimal places as needed.) σx = (Round to two decimal places as needed.) Hx= x = ■ (c) Compute the mean and standard deviation, using μx = np and ox=√/np(1-p). (Round to two decimal places as needed.) (Round to two decimal places as needed.) || (d) Draw a graph of the probability distribution and comment on its shape. Which graph below shows the probability distribution? OA. 0.5- AP(x) 0.25- Q The binomial probability distribution is ▼ OB. APX) 0.5 0.25- Q O C. APX) 0.5- 0.25- Q O D. 0.5 APX) 0.25-1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
Related questions
Question
![**Educational Content: Binomial Probability Distribution**
Use \( n = 6 \) and \( p = 0.7 \) to complete parts (a) through (d) below.
---
**(a) Construct a binomial probability distribution with the given parameters.**
\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & \text{ } \\
1 & \text{ } \\
2 & \text{ } \\
3 & \text{ } \\
4 & \text{ } \\
5 & \text{ } \\
6 & \text{ } \\
\hline
\end{array}
\]
*(Round to four decimal places as needed.)*
---
**(b) Compute the mean and standard deviation of the random variable using**
\[
\mu_X = \sum [x \cdot P(x)] \quad \text{and} \quad \sigma_X = \sqrt{\sum [x^2 \cdot P(x)] - \mu_X^2}
\]
- \( \mu_X = \) ____ (Round to two decimal places as needed.)
- \( \sigma_X = \) ____ (Round to two decimal places as needed.)
---
**(c) Compute the mean and standard deviation, using**
\[
\mu_X = np \quad \text{and} \quad \sigma_X = \sqrt{np(1-p)}
\]
- \( \mu_X = \) ____ (Round to two decimal places as needed.)
- \( \sigma_X = \) ____ (Round to two decimal places as needed.)
---
**(d) Draw a graph of the probability distribution and comment on its shape.**
**Which graph below shows the probability distribution?**
- **Option A:** A graph with a right-skewed distribution.
- **Option B:** A graph with a peak at \( x = 4 \), symmetrically decreasing.
- **Option C:** A graph with a peak at \( x = 3 \), symmetrically decreasing.
- **Option D:** A graph with a left-skewed distribution.
The binomial probability distribution is [Select: Option A, B, C, D].
*(Based on discussing which graph most accurately portrays the computed probabilities with \( n = 6 \) and \( p = 0.7 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faba41a1d-d1f3-4790-876b-aeeed0dbb2e9%2F52446760-2259-46eb-b8ce-870f0bda5ba1%2Fx62izc_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Binomial Probability Distribution**
Use \( n = 6 \) and \( p = 0.7 \) to complete parts (a) through (d) below.
---
**(a) Construct a binomial probability distribution with the given parameters.**
\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & \text{ } \\
1 & \text{ } \\
2 & \text{ } \\
3 & \text{ } \\
4 & \text{ } \\
5 & \text{ } \\
6 & \text{ } \\
\hline
\end{array}
\]
*(Round to four decimal places as needed.)*
---
**(b) Compute the mean and standard deviation of the random variable using**
\[
\mu_X = \sum [x \cdot P(x)] \quad \text{and} \quad \sigma_X = \sqrt{\sum [x^2 \cdot P(x)] - \mu_X^2}
\]
- \( \mu_X = \) ____ (Round to two decimal places as needed.)
- \( \sigma_X = \) ____ (Round to two decimal places as needed.)
---
**(c) Compute the mean and standard deviation, using**
\[
\mu_X = np \quad \text{and} \quad \sigma_X = \sqrt{np(1-p)}
\]
- \( \mu_X = \) ____ (Round to two decimal places as needed.)
- \( \sigma_X = \) ____ (Round to two decimal places as needed.)
---
**(d) Draw a graph of the probability distribution and comment on its shape.**
**Which graph below shows the probability distribution?**
- **Option A:** A graph with a right-skewed distribution.
- **Option B:** A graph with a peak at \( x = 4 \), symmetrically decreasing.
- **Option C:** A graph with a peak at \( x = 3 \), symmetrically decreasing.
- **Option D:** A graph with a left-skewed distribution.
The binomial probability distribution is [Select: Option A, B, C, D].
*(Based on discussing which graph most accurately portrays the computed probabilities with \( n = 6 \) and \( p = 0.7 \).
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