Answer:
[tex]P(x > 4.5)= 0.983943[/tex]
Step-by-step explanation:
Given
[tex]\mu = 6[/tex]
[tex]\sigma = 0.7[/tex]
Required
[tex]P(x > 4.5)[/tex]
Start by calculating the z score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So:
[tex]z = \frac{4.5 - 6}{0.7}[/tex]
[tex]z = \frac{-1.5}{0.7}[/tex]
[tex]z = -2.143[/tex]
So, we have:
[tex]P(x > 4.5)= 1 - P(x < 4.5)[/tex]
This gives:
[tex]P(x > 4.5)= 1 - P(x < z)[/tex]
[tex]P(x > 4.5)= 1 - P(x < -2.143)[/tex]
Using the z score probability table, we have:
[tex]P(x > 4.5)= 1 - 0.016057[/tex]
[tex]P(x > 4.5)= 0.983943[/tex]
