Answered: Consider a population with a mean μ=162…

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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Consider a population with a mean μ=162 and standard deviation σ=72. Suppose random samples of size n=50 are selected from this population.

a) What is the mean of the distribution of the sample mean?
μx̅=
b) What is the standard error of the mean? (2 decimal places)
σx̅=

In the following questions, round the standard error and z-scores to exactly 2 decimal places before determining probabilities. Report probabilities accurate to at least 3 decimal places.

2. What is the probability that a randomly selected sample mean is:
a) greater than 155?
b) less than 161.4?
c) greater than 155 and less than 161.4?
d) greater than 155 given less than 161.4?
e) greater than 155 or greater than 161.4?

3. Between what values would you expect to find the middle 56% of the sample means? Round to the nearest integer.
Between______and___________ .

4. Why are we able to use the normal distribution in the calculations above?

Becasuse the standard error is large enough
Because the sample mean is large enough
Because the sample size is large enough
Because the original population is normal

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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