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Please answer number 2. Make sure to show work! Thanks!

Please answer number 2. Make sure to show work! Thanks!

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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Please answer number 2. Make sure to show work! Thanks! 

### Statistical Literacy in Binomial Distributions **1. Statistical Literacy: What does the expected value of a binomial distribution with _n_ trials tell you?** The expected value of a binomial distribution with _n_ trials represents the mean number of successes you would expect if you were to conduct an experiment many times. **2. Statistical Literacy: Consider two binomial distributions, with _n_ trials each. The first distribution has a higher probability of success on each trial than the second. How does the expected value of the first distribution compare to that of the second?** If the first distribution has a higher probability of success on each trial compared to the second, then the expected value of the first distribution will be higher than that of the second. ### Basic Computation: Expected Value and Standard Deviation **3. Basic Computation: Expected Value and Standard Deviation** Consider a binomial experiment with _n_ = 8 trials and _p_ = 0.20. (a) **Find the expected value and the standard deviation of the distribution.** To find the expected value (mean) \(E\) and the standard deviation \( \sigma \): - Expected value \(E\) = _n_ × _p_ - Standard deviation \( \sigma \)= √(_n_ × _p_ × (1 - _p_)) Here, \(E = 8 \times 0.20 = 1.6\). For standard deviation: \( \sigma = \sqrt{8 \times 0.20 \times 0.80} = \sqrt{1.28} \approx 1.13 \). (b) **Interpretation: Would it be unusual to obtain 5 or more successes? Explain. Confirm your answer by looking at the binomial probability distribution table.** It would be unusual to obtain 5 or more successes because the expected value is 1.6 with a standard deviation of approximately 1.13. Using the binomial probability distribution, you would calculate the probability of obtaining 5 or more successes. If this probability is very low, it confirms the result is unusual. **4. Basic Computation: Expected Value and Standard Deviation** Consider a binomial experiment with _n_ = 20 trials and _p_ = 0.40. (a) **Find the expected value and the standard deviation of the distribution.**
Transcribed Image Text:### Statistical Literacy in Binomial Distributions **1. Statistical Literacy: What does the expected value of a binomial distribution with _n_ trials tell you?** The expected value of a binomial distribution with _n_ trials represents the mean number of successes you would expect if you were to conduct an experiment many times. **2. Statistical Literacy: Consider two binomial distributions, with _n_ trials each. The first distribution has a higher probability of success on each trial than the second. How does the expected value of the first distribution compare to that of the second?** If the first distribution has a higher probability of success on each trial compared to the second, then the expected value of the first distribution will be higher than that of the second. ### Basic Computation: Expected Value and Standard Deviation **3. Basic Computation: Expected Value and Standard Deviation** Consider a binomial experiment with _n_ = 8 trials and _p_ = 0.20. (a) **Find the expected value and the standard deviation of the distribution.** To find the expected value (mean) \(E\) and the standard deviation \( \sigma \): - Expected value \(E\) = _n_ × _p_ - Standard deviation \( \sigma \)= √(_n_ × _p_ × (1 - _p_)) Here, \(E = 8 \times 0.20 = 1.6\). For standard deviation: \( \sigma = \sqrt{8 \times 0.20 \times 0.80} = \sqrt{1.28} \approx 1.13 \). (b) **Interpretation: Would it be unusual to obtain 5 or more successes? Explain. Confirm your answer by looking at the binomial probability distribution table.** It would be unusual to obtain 5 or more successes because the expected value is 1.6 with a standard deviation of approximately 1.13. Using the binomial probability distribution, you would calculate the probability of obtaining 5 or more successes. If this probability is very low, it confirms the result is unusual. **4. Basic Computation: Expected Value and Standard Deviation** Consider a binomial experiment with _n_ = 20 trials and _p_ = 0.40. (a) **Find the expected value and the standard deviation of the distribution.**
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