Question

Let X be a Normally distributed random variable with mean μ = 0 and σ = 2. What is the probability that X is more than 0.5?

Answer 1

To find the probability that X is more than 0.5 in a Normally distributed random variable with mean μ = 0 and σ = 2, we can standardize the value 0.5 and calculate the probability using a standard normal distribution table or a calculator. The probability is approximately 0.5987.

Step-by-step explanation:

To find the probability that X is more than 0.5, we need to calculate the area under the curve of the normal distribution to the right of 0.5.

First, we need to standardize the value 0.5 using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Plugging in the values, we have z = (0.5 - 0) / 2 = 0.25. Now we can find the probability using a standard normal distribution table or a calculator. The probability that X is more than 0.5 is approximately 0.5987.