Answer:
[tex]P(X>34) = 0.9889[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 50
Standard Deviation, σ = 7
We are given that the distribution of random variable X is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(X greater than 34)
[tex]P( X > 34) = P( z > \displaystyle\frac{34 - 50}{7}) = P(z > -2.2857)[/tex]
[tex]= 1 - P(z \leq -2.2857)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(X>34) = 1 - 0.0111= 0.9889= 98.89\%[/tex]
The attached image shows the normal curve.
