Answered: approximating normal distribution

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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Ten percent of Americans are allergic to ragweed. Suppose a random sample of 200 people is selected.

1. Identify n

2. Identify p (Round to 2 decimal places)

3. Identify 1 – p (Round to 2 decimal places)

4. Evaluate np and n(1 – p). Is it appropriate to use the normal distribution to approximate the binomial distribution? (Round to 2 decimal places)

np = n(1 – p) = Enter Y or N

If your answer to part (d) above is “yes” answer the following questions.

5. What is the mean and standard deviation of the approximating normal distribution? (Round to 2 decimal places)

µ = σ =

6. Find the probability that exactly 10 will be allergic to ragweed (Round to 4 decimal places)

7. Find the probability that at most 10 will be allergic to ragweed (Round to 4 decimal places)

8. Find the probability at least 10 will be allergic to ragweed (Round to 4 decimal places)

9. Find the probability that less than 10 will be allergic to ragweed (Round to 4 decimal places)

10. Find the probability that more than 10 will be allergic to ragweed (Round to 4 decimal places)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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