Question

For a random variable X following a normal distribution with mean 4 and standard deviation 5 (i.e.,X∼N(4,5)), what is the maximum value of X in the bottom quartile?

A. 1
B. 2
C. 3
D. 4

Answer 1

In a normal distribution with mean 4 and standard deviation 5, the maximum value in the bottom quartile is 1.

Step-by-step explanation:

In a normal distribution with mean 4 and standard deviation 5, the bottom quartile represents the lowest 25% of the data. To find the maximum value in the bottom quartile, we need to find the value of X that is greater than the bottom 25% of the data. This can be calculated using the z-score formula. The z-score for the bottom quartile is -0.674, so we can find the corresponding X value by solving for X in the equation -0.674 = (X - 4) / 5.

Solving this equation, we find that X is approximately 1.63. Since we are looking for the maximum value in the bottom quartile, the answer is A. 1.