SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.7 years, and standard deviation of 1.9 years. If 3 items are picked at random, 1%

Algebra ->  Finance -> SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.7 years, and standard deviation of 1.9 years. If 3 items are picked at random, 1%       Log On


   

Question 1184571: A manufacturer knows that their items have a normally distributed lifespan,
with a mean of 13.7 years, and standard deviation of 1.9 years.
If 3 items are picked at random, 1% of the time their mean life will be less
than how many years?
Give your answer to one decimal place.
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 13.7 years, and standard deviation of 1.9 years.
If 3 items are picked at random, 1% of the time their mean life will be less
than how many years?
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 3 we must divide the standard deviation by √3.

Since the probability 1% is given, we use the inverse normal  

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

Make the screen read like this:

     invNorm
area:0.01
μ:13.7
σ:1.9/√(3)      <-- the √( key is 2ND x2
Paste

Use the down arrow key to highlight Paste
Press ENTER

Read this:

invNorm(0,01,13.7,1.9/√(3))

Press ENTER
 
Read 11.14807661

Round to 11.1

Edwin