Assume that x is normally distributed random variable with a mean equal to 13.4 and a standard deviation equal to 3.6. Assume also that P(x a) = 0.05. The value of a must be 19.322.

Question

Assume that x is normally distributed random variable with a mean equal to 13.4 and a standard deviation equal to 3.6. Assume also that P(x > a) = 0.05. The value of a must be 19.322.

Quizplus · Accepted Answer

For a normal distribution, the value of 'a' such that P(x > a) = 0.05 corresponds to the 95th percentile. Using the z-score formula, a = mean + z * standard deviation. The z-score for 0.05 in the upper tail is approximately 1.645. Thus, a = 13.4 + 1.645 * 3.6 ≈ 19.322.

Assume That X Is Normally Distributed Random Variable with a Mean