**Title: Converting Binomial Distribution to Normal Approximation**According to the Gallup poll, 40% of Americans aged 18 and older stated that they had read at least six books within the past year. You conduct a random sample of 200 Americans aged 18 or older. **Objective:** Approximate the probability that between 70 and 90, inclusive, have read at least six books within the past year using normal approximation.**Explanation:** This is a classic example of applying the binomial to normal approximation. We begin by identifying the parameters for the binomial distribution: - \(n = 200\) (the number of trials)- \(p = 0.4\) (the probability of success)Next, we calculate the mean (\(\mu\)) and standard deviation (\(\sigma\)) for the normal distribution approximation: - Mean: \(\mu = np = 200 \times 0.4 = 80\)- Standard Deviation: \(\sigma = \sqrt{np(1-p)} = \sqrt{200 \times 0.4 \times 0.6} \approx 6.93\)We are interested in the probability that between 70 and 90, inclusive, read at least six books. To find this, we convert the range values to z-scores and use the standard normal distribution table.

Answered: (Binomial to Normal) According to the…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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(Binomial to Normal) According to the Gallup poll, 40% of Americans 18 year-old or older stated that they had read at least 6 books within the past year. You conduct a random sample of 200 Americans 18 year- old or older.