x is a normally distributed random variable with a mean of 8.20 and variance of 4.41, and P(x b) = 0.08. What is the value of b?
A) 3.409
B) 3.448
C) 3.452
D) 11.914

Question

x is a normally distributed random variable with a mean of 8.20 and variance of 4.41, and P(x > b) = 0.08. What is the value of b?
A) 3.409
B) 3.448
C) 3.452
D) 11.914

Quizplus · Accepted Answer

First, we need to standardize the normal distribution using the formula: Z = (X - μ) / σ where μ is the mean and σ is the standard deviation In this case, we have: μ = 8.2 σ = sqrt(4.41) = 2.1 Z = (b - 8.2) / 2.1 Next, we need to find the z-score that corresponds to a probability of 0.08 in the right tail of the standard normal distribution. We can use a standard normal distribution table or calculator to find that z = 1.405. Therefore, we have: 1.405 = (b - 8.2) / 2.1 Solving for b, we get: b = 1.405 * 2.1 + 8.2 = 11.448 Since we are looking for P(x > b), we can subtract the cumulative area up to b (which is the same as P(x <= b)) from 1: P(x > b) = 1 - P(x <= b) Using a normal distribution table or calculator, we can find: P(x <= 11.448) = 0.92 Therefore, P(x > b) = 1 - P(x <= b) = 0.08 So, b = 11.448 is the correct answer, and the closest choice in the options is B.

X Is a Normally Distributed Random Variable with a Mean