If X is normally distributed with μ = 20 and σ = 5,find such that P(X
)= 0.025.
A) 18.6
B) 21.96
C) 27.2
D) 29.8
E) 31.6

Question

If X is normally distributed with μ = 20 and σ = 5,find  such that P(X > 
)= 0.025.
A) 18.6 
B) 21.96 
C) 27.2 
D) 29.8 
E) 31.6

Quizplus · Accepted Answer

We need to find the value of x such that P(X > x) = 0.025.
Using the properties of normal distribution, we can find the corresponding z-score:
z = (x - μ) / σ
z = (x - 20) / 5
From the standard normal distribution table, we can find the z-score corresponding to a cumulative area of 0.025 in the right-tail:
z = 1.96
Substituting the values, we get:
1.96 = (x - 20) / 5
x - 20 = 9.8
x = 29.8
Therefore, the value of x is 29.8, which is closest to option D.

If X Is Normally Distributed with μ = 20 and σ