Ask AI: Suppose is a normally distributed random variable with mean μ = 0 and standard deviation σ = 1. Find the probability that x < 0.64.

To find the probability that x < 0.64 for a normally distributed random variable with mean μ = 0 and standard deviation σ = 1, we can use the standard normal (z) table. First, you need to convert the given value of x (0.64) into a z-score. Since the mean (μ) is 0 and the standard deviation (σ) is 1, the z-score is the same as x: z = (x - μ) / σ z = (0.64 - 0) / 1 z = 0.64 Now, we will look up the probability associated with z = 0.64 in the standard normal (z) table. You will see two sets of numbers in the table, one on the vertical axis and one on the horizontal axis. Search for the first two digits of the z-score (0.6) along the vertical axis, and the second decimal place (0.04) along the horizontal axis. The intersection of the two will give you the probability. The probability of x < 0.64 for a standard normal distribution, which corresponds to a z-score of 0.64, is approximately 0.7389. So, the probability that x < 0.64 is approximately 0.7389 or 73.89%.