Given:
- The Mean:
[tex]\mu=19.9[/tex]
- The Standard Deviation:
[tex]\mu=33.1[/tex]
You have to find:
[tex]P(x>8.9)[/tex]
You need to find the z-statistic using this formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
In this case:
[tex]x=8.9[/tex]
Then:
[tex]z=\frac{8.9-19.9}{33.1}\approx-0.332[/tex]
You need to find:
[tex]P(z>-0.332)[/tex]
By symmetry, this is equal to:
[tex]P(z<0.0332)[/tex]
Using the Normal Distribution Table, you get:
[tex]P(z<0.0332)=0.6293[/tex]
Hence, the answer is:
[tex]P(x>8.9)=0.6293[/tex]
