Answered: sample mean greater than 34? b)…

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

A sample of n = 4 scores is selected from a population with µ = 30 and s = 8. Which is more likely,

a) selecting a sample mean greater than 34?

b) selecting a sample mean with a z-score greater than z = 2.00?

Assume the population is a normal distribution.

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

(a)

The probability that selecting a sample mean greater than 34 is:

By using the standard normal table,

Hence, the required probability that selecting a sample means greater than 34 is 0.3085.

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