Question

Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P (Upper X greater than 34 )

Answer 1

Answer:

$P(X>34) = 0.9889$

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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(X greater than 34)

$P( X > 34) = P( z > \displaystyle\frac{34 - 50}{7}) = P(z > -2.2857)$

$= 1 - P(z \leq -2.2857)$

Calculation the value from standard normal z table, we have,  

$P(X>34) = 1 - 0.0111= 0.9889= 98.89\%$

The attached image shows the normal curve.