Question

Stats Help!!

Answer 1

The distribution of salaries in a company is skewed to the right. That is, most employees make a small amount of money while a few executives earn much higher salaries.

a) What would a sampling distribution of sample size 3 look like?
b) What would a sampling distribution of sample size 10 look like?
c) What would a sampling distribution of sample size 50 look like?

How would I do this problem?

The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. You take a random sample of a dozen eggs.

a) What are the mean and standard deviation of the sampling distribution of sample size 12?
b) What is the probability that the mean weight of the eggs in the sample will be less than 2.2 ounces?

I found the mean and SD, but how would I do part B?

Answer 2

@kropot72 Can you please help me?

Answer 3

Knowledge of the Central Limit Theorem is needed to answer the first question. Have you studied the CLT?

Answer 4

If the sampling size gets bigger, the sampling distribution becomes more even?

Answer 5

If the sampling size gets bigger then the sample statistic is more likely to resemble the the population parameter

Answer 6

Ohh I get it. So the sample size of 50 would be evenly distributed?

Answer 7

The CLT indicates that for sample sizes greater than 30, the distribution of the sample means is approximately normal, regardless of the distribution of the parent population.

Answer 8

Okay that makes sense thank you! How would I do the second one part B?

Answer 9

Like what equation would I use? Would i Use the normalcdf function for that?

Answer 10

For the second question, what are your results for the mean and the SD of the sampling distribution?

Answer 11

Mean is 2.25 and the SD is .057

Answer 12

I get 2.25 for the mean and 0.058 for the SD.
For part b), find the z-score for X = 2.2 and sigma = 0.058. Then you can use a standard normal distribution table to find the required probability.

Answer 13

Oh so why am I finding the z-score if this is probability? I thought z-score was only for telling how many SDs away something is? Sorry I am just wondering/

Answer 14

The z-score enables you to use a standardized table for the normal distribution. This table gives values of cumulative probability against standardized values of SD.

Answer 15

\[\large z=\frac{X-\mu}{\sigma}=\frac{2.2-2.25}{0.058}\]

Answer 16

-0.866

Answer 17

So essentially the z-score can help find probability as well? Thank you btw

Answer 18

Correct. My value for z is close to -0.86. You can use the table here if you like:
http://www.math.bgu.ac.il/~ngur/Teaching/probability/normal.pdf

Answer 19

Okay, thank you very much :)

Answer 20

Good work! You're welcome :)