Answered: For a certain year, the average annual…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Question

For a certain year, the average annual salary in Pennsylvania was $25,000.

Assume that the salaries were normally distributed for a certain group of wage earners and that the standard deviation of this group was $4400.

Use the formulas

Z= (x-μ) / σ

Z= (x̄ - μ) ÷ (μ / √n)

a) Find the probability that, a randomly selected individual earned less than $26,000.

b) Find the probability that, for a randomly selected sample of 25 individuals, the mean salary was less than $26000.

c) Why is the probability for part b higher than the probability for part a?

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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