Sample Mean and Population Mean: Standard Deviation

Please explain how to set up and solve. I have attempted to answer, please let me know if right or wrong...

A sample of n= 36 scores is selected form a population with o= 12. if the sample mean of M=56 produces a z score of z= +3.00 then what is the population mean?
* 56
*52 (is this correct?)
* 54
*50

A sample of n= 9 scores is obtained from a population with u= 70 and o= 18. if the sample mean is M=76, what is the z-score for the sample mean?
* z= 0.50
*z= 1.00
*z= 0.33 ( is this correct?)
* z= 3.00

A random sample of n=4 scores is obtained from a normal population with u= 30 and o= 8. what is the probability that the sample mean will be smaller than M= 22?
* 0.00003
* 0.1587 ( is this correct?)
* 0.3085
* 0.0228

a random sample of n= 9 scores is obtained from a normal population with u= 40 and o= 18. what is the probability that the sample mean will be greater than M= 43?
* 0.1587
*0.0228
*0.4325 ( is this correct?)
* 0.3085

Solution Preview

1.
=> M-u = z*o/sqrt(n)
=> 56 - u = 3*12/sqrt(36)
=> u = 56 - 3*12/6 = 50

2.
z = ...

Solution Summary

A few problem related to sample and population mean are solved here.

A sample mean, sample size, and population standard deviation are given. Use the P-value approach to perform a one-mean z-test about the mean of the population from which the sample was drawn.
x bar= 78, n = 28, sigma = 11, Hnought: mu=72, Hone: mu>72 , alpha = 0.01
First find the proper z value then use this to find the

What is the sampling distribution of samplemeans?
What is the mean of the sampling distribution of samplemeans?
What is its standard deviation?
How is that standard deviation affected by the sample size?
What does the central limit theorem state about that distribution?

If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what would be the mean, variance, standard deviationand shape of the distribution of samplemeans? Give reasons for your answers.
Note: Variance is the square of the standard d

If you were designing a study which group, a population or a sample, would you collect data from and why? Provide an explanation regarding whether or not the standard deviation is a biased or unbiased estimate. When comparing the standard deviation to the variance, which do you prefer to interpret and why do you feel this way?

Suppose that we want to estimate the mean germination time of strawberry seeds. The germination times for the sample of strawberries we choose has a mean of days and a standard deviation of days. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements