There are 8000 students at the University of Tennessee at Ch

There are 8,000 students at the University of Tennessee at Chattanooga. The average age of all the students is 24 years with a standard deviation of 9 years. A random sample of 36 students is selected.

Solution

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TAH answered 8 years ago

First I am assuming the population is a standard normal. I can do this because it is such a large population.

A. Standard error = standard div/ square root of the population size = 9/(square root of 36)= 9/6= 1.5

For parts B and C I used a standard normal table. It is also known as a Z table.

B. First I find my z value. Z = (given value - population mean)/standard error = (19.5-24)/1.3 = -3.00

Using that z value, I look on the table for -3.00. The value is so extreme it is at the very end of my table, p=.0013. Now, this is the confusing part. I have found the probability that the sample mean is SMALLER then 19.5. I need to flip answer to get the probability that the sample mean is LARGER. 1-.0001=.9987

So final answer is .9987.

C. This is a fun one.

Find two z values.

z1=(25.5-24/1.5)=1
z2=(27-24/1.5)=2

Now, since the Z table is cumulative, I simple subtract z1 from z2.

z2 - z1 = .9772 - .8413 = .1359.