# 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

https://brainmass.com/statistics/probability/sample-mean-and-population-mean-standard-deviation-584638

#### 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.

Sampling Distribution, Mean and Standard Deviation

See attachment for better symbol representation.

1) A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. The standard deviation σ of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is know to equal 2 pounds per square inch, and the strength measurements are normally distributed.

a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?

b) If the mean of the population of strength measurements is 21 pounds per square inch, what is the approximate probability that, for a random sample of n = 10 test pieces of paper, ¯x < 20?

c) What value would you select for the mean paper strength μ in order that P (¯x < 20) be equal to .001?

2) Suppose a random sample of n = 25 observations is selected from a population that is normally distributed, with mean equal to 106 and standard deviation equal to 12?

a) Give the mean and standard deviation of the sampling distribution of the sample mean ¯x.

b) Find the probability that ¯x exceeds 110

c) Find the probability that the sample mean deviates from the population mean μ = 106 by no more than 4.