Answered: Explain why X can be modeled by a…

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

Suppose that 65% of high school students eat breakfast before going to school. A random sample of 500 high school students were surveyed. Let X = the number of high school students in a random sample size of 500 who eat breakfast before going to school.

1. Explain why X can be modeled by a binomial distribution even though the sample was selected without replacement.

2. Use a binomial distribution to estimate the probability that 300 or fewer high school students in the sample eat breakfast before going to school.

3. Justify why X can be approximated by a Normal distribution.

4. Use a Normal distribution to estimate the probability that 300 or fewer high school students in the sample eat breakfast before going to school.

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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