SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.9 years, and standard deviation of 2 years. If you randomly purchase 22 items, wha

Algebra ->  Finance -> SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.9 years, and standard deviation of 2 years. If you randomly purchase 22 items, wha      Log On


   

Question 1184845: A manufacturer knows that their items have a normally distributed lifespan,
with a mean of 13.9 years, and standard deviation of 2 years.
If you randomly purchase 22 items, what is the probability that their mean
life will be longer than 15 years? (Give answer to 4 decimal places.)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A manufacturer knows that their items have a normally distributed lifespan,
with a mean of 13.9 years, and standard deviation of 2 years.
If you randomly purchase 22 items, what is the probability that their mean
life will be longer than 15 years? (Give answer to 4 decimal places.)
The rule is:

You must use the t-distribution when working problems when the population
standard deviation (σ) is not known and the sample size is small (n<30).
General Correct Rule: If σ is not known, then using t-distribution is
correct. If σ is known, then using the normal distribution is correct.

In this problem, σ is known, so we use the normal distribution.  However,
since the sample size is 22 we must divide the standard deviation by √22.

On your TI-84, press ON CLEAR 2ND VARS 3

Make the screen read like this:

     normalcdf
lower:15
upper:99999999
μ:13.9
σ:2/√(22)      <-- the √ key is 2ND x2
Paste

Use the down arrow key to highlight Paste
Press ENTER

Read this:

normalcdf(15,13.9,2/√(22))

Press ENTER
 
Read 0.0049439287

Round to 0.0049

Edwin