Question

For a normal population with an average of 60 and a standard deviation of 12 what is the probability of selecting a random sample of 36 scores with a sample mean greater than 64? p(M greater than 64)?

a 50%

b .9772 or 97.72 %

c. .8777 or 87.77%

d. .0228 or 2.28%

A population has a mean of 50 and a standard deviation of 5, find the z-score that corresponds to a sample mean of M=55 for a sample size of 33.

a. 33

b. 5.75

c. 5

d. need more info

A population has a mean of 50 and a standard deviation of 5, find the z-score that corresponds to a sample mean of M=55 for a sample size of 10.

a. 5

b. 2.5

c. 10

d. 2.236

Answer 1

We use the following property of normal distribution

If we have a sample of size from a normal population with mean and standard deviation , the sample mean has normal distribution with mean and standard deviation .

Also has standard normal distribution.

Answer to question 1.

We have sample from normal population with mean and standard deviation . Also the size of sample is given to be . We want to find probability that M, the sample mean is greater than 64.

So the answer is d. 0.0228 or 2.28%.

_____________________________

To calculate the z-score,we have to find the difference between sample mean and the population mean, and divide it by the standard deviation of sample mean.

That is z-score is where M is the sample mean , is the mean of population, is the standard deviation and n is the sample size

Answer to question 2.

We have sample from population with mean of 50 and a standard deviation of 5. The size of sample is 33 and sample mean M=55.

The Z score is given by

So the answer is b.   5.75 .

Answer to question 3.

We have sample from population with mean of 50 and a standard deviation of 5. The size of sample is 10 and sample mean M=55.

The Z score is given by

So all the answers given as options are wrong. The z score is