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2. Use the binomial table and graph for n = 5, p = 0.50 to answer the following: a. What is the shape of the binomial distribution when p = 0.50? b. Use the Excel table and your TI-84 to find the mean and standard deviation of this binomial probability distribution. (Enter the probability column without rounding) Mean = Standard Deviation = c. Now use the binomial formulas below to find the mean and standard deviation when n= 5 and p= 0.50.

2. Use the binomial table and graph for n = 5, p = 0.50 to answer the following: a. What is the shape of the binomial distribution when p = 0.50? b. Use the Excel table and your TI-84 to find the mean and standard deviation of this binomial probability distribution. (Enter the probability column without rounding) Mean = Standard Deviation = c. Now use the binomial formulas below to find the mean and standard deviation when n= 5 and p= 0.50.

MATLAB: An Introduction with Applications
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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EXCEL CHART:

X P(X)
0 0.903921
1 0.092237
2 0.003765
3 7.68E-05
4 7.84E-07
5 3.2E-09
### Using the Binomial Table and Graph for \( n = 5, p = 0.50 \) #### 2. Answer the following: **a. What is the shape of the binomial distribution when \( p = 0.50 \)?** *Response:* The shape of the binomial distribution when \( p = 0.50 \) is symmetric. **b. Use the Excel table and your TI-84 to find the mean and standard deviation of this binomial probability distribution. (Enter the probability column without rounding.)** * Mean = * Standard Deviation = *Note: Instructions imply calculating these values using tools like Excel or a TI-84 calculator.* **c. Now use the binomial formulas below to find the mean and standard deviation when \( n = 5 \) and \( p = 0.50 \).** * Mean \( \mu = n \cdot p \) * Standard Deviation \( \sigma = \sqrt{npq} \) Where \( q = 1 - p \) is the probability of failure. **d. What do you notice about your solutions to parts b and c?** *Response:* The solutions to parts b and c are expected to be the same since the calculations in part c use the binomial formulas which should yield the exact same results as those obtained using tools like Excel or a TI-84 calculator. #### Explanation of Binomial Formulas: - The mean \( \mu \) of a binomial distribution is calculated by multiplying the number of trials \( n \) by the probability of success \( p \). - The standard deviation \( \sigma \) is found by taking the square root of \( npq \), where \( q = 1 - p \). This exercise demonstrates how to calculate the mean and standard deviation of a binomial distribution using both computational tools and mathematical formulas.
Transcribed Image Text:### Using the Binomial Table and Graph for \( n = 5, p = 0.50 \) #### 2. Answer the following: **a. What is the shape of the binomial distribution when \( p = 0.50 \)?** *Response:* The shape of the binomial distribution when \( p = 0.50 \) is symmetric. **b. Use the Excel table and your TI-84 to find the mean and standard deviation of this binomial probability distribution. (Enter the probability column without rounding.)** * Mean = * Standard Deviation = *Note: Instructions imply calculating these values using tools like Excel or a TI-84 calculator.* **c. Now use the binomial formulas below to find the mean and standard deviation when \( n = 5 \) and \( p = 0.50 \).** * Mean \( \mu = n \cdot p \) * Standard Deviation \( \sigma = \sqrt{npq} \) Where \( q = 1 - p \) is the probability of failure. **d. What do you notice about your solutions to parts b and c?** *Response:* The solutions to parts b and c are expected to be the same since the calculations in part c use the binomial formulas which should yield the exact same results as those obtained using tools like Excel or a TI-84 calculator. #### Explanation of Binomial Formulas: - The mean \( \mu \) of a binomial distribution is calculated by multiplying the number of trials \( n \) by the probability of success \( p \). - The standard deviation \( \sigma \) is found by taking the square root of \( npq \), where \( q = 1 - p \). This exercise demonstrates how to calculate the mean and standard deviation of a binomial distribution using both computational tools and mathematical formulas.
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