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 = ...

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