Question

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.9332.

a. 120

b. 1.50

c. 374

d. 370

Answer 1

Given that, X be normally distributed with mean (μ) = 250 and standard deviation (σ) = 80

We want to find the value of x such that, P(X ≤ x) = 0.9332

First we find, z-score such that, P(Z ≤ z) = 0.9332

Using standard normal z-table we get, z-score corresponding are under the normal curve of 0.9332 is, z = 1.50

we know,

Z = (x - μ) / σ

=> x = zσ + μ

=> x = (1.50 * 80) + 250

=> x = 120 + 250

=> x = 370

=> P(X ≤ 370) = 0.9332

Therefore, required value of x is 370.

Answer : d) 370