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.

... As samples are drawn from normal population, sample mean distribution will follow normal distribution with mean=18 and standard deviation=0.5774. ...

... The mean contribution is $150 and the standard deviation of the sample is $20. Construct a 98 percent confidence interval for the population mean. ...

... are characteristic of the sample data, eg, the sample mean, standard deviation, variance, etc ... is making inferences or conclusions about the population by making ...

... c) Find the probability that the sample mean deviates from the population mean ยต = 106 ... To check on the quality of the paper, a random sample of 10 ...

... 15 The use of the finite population correction factor when sampling without replacement from finite ... a.) increase the standard error of the mean. ...

... is u = 1020 and a population standard deviation is o = 100. What is the probablity that a random sample of 75 students will provide a sample mean SAT score ...

... if the sample mean was used to estimate the population mean. ... the annual cost by taking a larger (than 45) sample. Populations and standard means are examined. ...

... If a random sample of n cases is drawn from a population with mean M and standard deviation s , then the sampling distribution of the mean (the distribution of ...