Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736.
A) −0.94
B) 0.94
C) 20.30
D) 29.70

Question

Quizplus · Accepted Answer

Using a standard normal table or calculator, we find that the z-score corresponding to the right-tail probability of 0.1736 is approximately 0.96. Thus, we have:

z = (x - µ)/σ = 0.96

Substituting the given values, we get:

(x - 25)/5 = 0.96

Solving for x, we obtain:

x = 4.8 + 25 = 29.8

Therefore, the value x such that P(X ≥ x) = 0.1736 is approximately 29.8. The closest choice is D, 29.70.

Let X Be Normally Distributed with Mean µ = 25