If x is normally distributed random variable with a mean of 8.20 and variance of 4.41, and that P(x b) = .08, then the value of b is:
A) 11.161
B) 3.409
C) 3.448
D) 3.452
E) 8.418

Question

If x is normally distributed random variable with a mean of 8.20 and variance of 4.41, and that P(x > b) = .08, then the value of b is:
A) 11.161
B) 3.409
C) 3.448
D) 3.452
E) 8.418

Quizplus · Accepted Answer

Given a normal distribution with a mean (μ) of 8.20 and a variance (σ^2) of 4.41, the standard deviation (σ) is the square root of the variance, which is 2.1. The probability P(x > b) = .08 corresponds to the upper tail of the normal distribution. Using the Z-table or standard normal distribution table, we find that the Z-score corresponding to a cumulative probability of 1 - .08 = .92 is approximately 1.41. To find the value of b, we use the Z-score formula: Z = (X - μ) / σ. Plugging in the values, 1.41 = (b - 8.20) / 2.1. Solving for b gives b ≈ 11.161.

If X Is Normally Distributed Random Variable with a Mean