Question

Consider a normal distribution with mean 39 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 39? (Round your answer to two decimal places.)

Answer 1

In a normal distribution, 50% of the values lie above the mean. Therefore, the probability that a value selected from a normal distribution with a mean of 39 is greater than 39 is simply 0.50 or 50%.

Step-by-step explanation:

The question is about finding the probability that a value selected at random from a normal distribution is greater than the mean. Given the normal distribution has a mean (μ) of 39 and a standard deviation (σ) of 3, we want to calculate P(X > 39).

In a normal distribution, the mean divides the curve into two equal halves. Therefore, the probability of a randomly selected value being greater than the mean is 0.50 or 50%. This is because 50% of the values in a normal distribution lie above the mean, and 50% lie below the mean. There is no calculation needed here as this is a property of a normal distribution's symmetry when the question is about the probability of being greater than the mean itself.