Question

Assume the random variable X is normally distributed with mean μ = 50 and standard deviation o=7. Compute th

probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.
P(54 ≤x≤69)
Click the icon to view a table of areas under the normal curve.

Answer 1

The probability P(54 ≤ x ≤ 69) is 0.2805 and the normal curve with the area corresponding to the probability shaded is added as an attachment

How to evaluate the probabilty

From the question, we have the following parameters that can be used in our computation:

Mean, μ = 50

Standard deviation, σ = 7

The probability is given as

P(54 ≤ x ≤ 69)

The standard score is calculated using

z = (x - μ)/σ

When x = 54, we have

z = (54 - 50)/7 = 0.5714

When x = 69, we have

z = (69 - 50)/7 = 2.7143

This means that

P(54 ≤ x ≤ 69) = P(0.5714 ≤ z ≤ 2.7143)

Using the z table of probabilities, we have

P(54 ≤ x ≤ 69) = 0.2805

Hence, the probability is 0.2805 and the area is added as an attachment