Salaries for teachers in a particular state have a mean of $ 49000 and a standard deviation of $ 5500. a. If we randomly select 12 teachers from that district, can you determine the sampling distribution of the sample mean? If yes, what is the name of the distribution? The mean? The standard error? b. If we randomly select 61 teachers from that district, can you determine the sampling distribution of the sample mean? 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 61, 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 61, 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?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question

Salaries for teachers in a particular state have a mean of $ 49000 and a standard deviation of $ 5500.

a. If we randomly select 12 teachers from that district, can you determine the sampling distribution of the sample mean?

  1. ? Yes No
  2. If yes, what is the name of the distribution?
  3. The mean?
  4. The standard error?

b. If we randomly select 61 teachers from that district, can you determine the sampling distribution of the sample mean?

  1. ? No Yes
  2. If yes, what is the name of the distribution?
  3. The mean?
  4. 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?

? 61 or 12

d. Assuming a sample size of 61, 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 61, 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?

Salaries for teachers in a particular state have a mean of $ 49000 and a standard deviation of $ 5500.
a. If we randomly select 12 teachers from that district, can you determine the sampling distribution of the sample mean?
If yes, what is the name of the distribution?
The mean?
The standard error?
b. If we randomly select 61 teachers from that district, can you determine the sampling distribution of the sample mean?
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 61, 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 61, 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?
Transcribed Image Text:Salaries for teachers in a particular state have a mean of $ 49000 and a standard deviation of $ 5500. a. If we randomly select 12 teachers from that district, can you determine the sampling distribution of the sample mean? If yes, what is the name of the distribution? The mean? The standard error? b. If we randomly select 61 teachers from that district, can you determine the sampling distribution of the sample mean? 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 61, 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 61, 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?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON