Answered: Assume a binomial probability…

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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Question

Assume a binomial probability distribution has p = .60 and n = 200.
a. what are the mean and standard deviation?
b. Is this situation one in which binomial probabilities can be approximated by the
normal probability distribution? Explain.

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.

Expert Solution

Step 1

The binomial probability distribution has p=0.60p=0.60 and n=200n=200.

Assume that the random variable x follows binomial distribution with p=0.60 and n=200.

The formula for mean in binomial distribution is,

μ=np

Where p is the probability of success and n is the number of trials.

The formula for standard deviation is,

Thus, the standard deviation is 6.93.

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