Assume that x is a normally distributed random variable with a mean equal to 13.4 and a standard deviation equal to 3.6. Given this information and that P(x a) = .05, the value of a must be 19.322.

Question

Assume that x is a normally distributed random variable with a mean equal to 13.4 and a standard deviation equal to 3.6. Given this information and that P(x > a) = .05, the value of a must be 19.322.

Quizplus · Accepted Answer

Given that x is normally distributed with a mean (μ) of 13.4 and a standard deviation (σ) of 3.6, and P(x > a) = .05, the value of a corresponds to the z-score for the 95th percentile (since 1 - .05 = .95). Using the z-table or a calculator for the standard normal distribution, we find the z-score that corresponds to the 95th percentile, and then use the formula a = μ + zσ to calculate the specific value of a. Given the parameters, the calculation accurately results in a value around 19.322, confirming the statement is true based on the properties of the normal distribution.

Assume That X Is a Normally Distributed Random Variable with a Mean