Salaries for teachers in a particular state have a mean of $ 46000 and a standard deviation of $ 5100. a. If we randomly select 42 teachers from that district, can you determine the sampling distribution of the sample mean? ? No Yes If yes, what is the name of the distribution? The mean? The standard error? b. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? ? Yes No If yes, what is the name of the distribution? The mean? The standard error? c. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer?d. Assuming a sample size of 42, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 42, what is the 90th percentile for the AVERAGE teacher’s salary? f. Assuming that teacher’s salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher’s salary?

Answered: Salaries for teachers in a particular…

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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Salaries for teachers in a particular state have a mean of $ 46000 and a standard deviation of $ 5100.

a. If we randomly select 42 teachers from that district, can you determine the sampling distribution of the sample mean?

? No Yes
If yes, what is the name of the distribution?
The mean?
The standard error?

b. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean?

? Yes No
If yes, what is the name of the distribution?
The mean?
The standard error?

c. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer?

d. Assuming a sample size of 42, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.)

e. Assuming a sample size of 42, what is the 90^th percentile for the AVERAGE teacher’s salary?

f. Assuming that teacher’s salaries are normally distributed, what is the 90^th percentile for an INDIVIDUAL teacher’s salary?

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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