Question 1184573
A manufacturer knows that their items have a normally distributed lifespan,
with a mean of 3.3 years, and standard deviation of 1.1 years.

If you randomly purchase 23 items, what is the probability that their mean
life will be longer than 3 years? (Give answer to 4 decimal places.)
<pre>
The rule is:

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

In this problem, &sigma; is known, so we use the normal distribution.  However,
since the sample size is 23 we must divide the standard deviation by √23.

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

Make the screen read like this:

     normalcdf
lower:3
upper:99999999
&mu;:3.3
&sigma;:1.1/√(23)      <-- the √ key is 2ND x<sup>2</sup>
Paste

Use the down arrow key to highlight Paste
Press ENTER

Read this:

normalcdf(3,99999999,3,3,1.1/√(23))

Press ENTER
 
Read 0.9045554884

Round to 0.9046

Edwin</pre>