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.)
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 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
μ:3.3
σ:1.1/√(23) <-- the √ key is 2ND x2
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