Given:
population mean (μ) = 14 inches
population standard deviation (σ) = 1 inch
sample size (n) = 126
Find: the probability that a sample mean > 16.2 inches
Solution:
To determine the probability, first, let's convert x = 16.2 to a z-value using the formula below.
[tex]x=\frac{\bar{x}-\mu}{\sigma\div\sqrt{n}}[/tex]
Let's plug into the formula above the given information.
[tex]z=\frac{16.2-14}{1\div\sqrt{126}}[/tex]
Then, solve.
[tex]z=\frac{2.2}{0.089087}[/tex][tex]z=24.6949[/tex]
The equivalent z-value of x = 16.2 is z = 24.6949
Since we are looking for the probability of greater than 16.2 inches, let's find the area under the normal curve to the right of z = 24.6949.
Based on the standard normal distribution table, the area from the center to z = 24.6949 is 0.5
Since we want the area to the right, let's subtract 0.5 from 0.5.
[tex]0.5-0.5=0[/tex]
Therefore, the probability that a sample mean of 126 men is greater than 16.2 inches is 0.
