Answered: Problem 1 Assume body heights (inches)…

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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Problem 1 Assume body heights (inches) for the population of 8-year old boys are: X-N(My 51, 0y = 3). If we choose 100 boys at random, what is the probability that their average height exceeds 50 inches? In the class, we apply the statistical knowledge about sampling distribution of the sample mean, denoted by X; that is, 8~NAxox/n) to solve this question analytically Now, please solve this question numerically computationally. That is, you should use simulation to compute a numerical approximate of the probability. Submit your R code and output with a brief description or explanation of your solution (Hint: you should use the rmorm function instead of pnorm function in R.)

Problem 2 Assume body heights (inches) for the population of 8-year old boys are: X-N(x = 51, 0x = 3). and body heights (inches) for the population of 8-year old girls are: Y-N(My = 53, ay = 3). If we randomly and independently choose 100 boys and 100 girls, what is the probability that the average height of the boys is greater than that of the girls? In the class, we apply the statistical knowledge about the linear combination of two sampling distributions of sample means to solve this question analytically. 1 Now, similar to Problem 1. please solve this question numerically computationally. That is, you should use simulation to compute a numerical approximation of the probability.

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