Answered: The heights of fully grown trees of 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

The heights of fully grown trees of a specific species are normally distributed, with a mean of

68.5

feet and a standard deviation of

6.50

feet. Random samples of size

are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution.

The mean of the sampling distribution is

μx=enter your response here.

The standard error of the sampling distribution is

σx=enter your response here.

(Round to two decimal places as needed.)

Choose the correct graph of the sampling distribution below.

68.5 72.0 65.0

A normal curve is over a horizontal x overbar axis labeled from 65.0 to 72.0 in increments of 1.7 and is centered on 68.5. A vertical line segment extends from the horizontal axis to the curve at 68.5.

0 2 -2

A normal curve is over a horizontal x overbar axis labeled from negative 2 to 2 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 0.

68.5 81.5 55.5

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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