A variable is normally distributed with a mean of 5.00 and a variance of 4.00. Calculate the probability of observing a value of negative 0.40 or less. That is, calculate P (Xi ≤ -0.40) given X is distributed as N(5,4). Use this excerpt from the cumulative distribution function for the standard normal random variable table to calculate your answer.
Cumulative Probabilities for a Standard Normal Distribution
P(Z ≤x) = N(x) for x ≥ 0 or P(Z ≤ z) = N(z) for z ≥ 0
A is correct. First, standardize the value of interest, -0.40, for the given normal distribution:
Z = (X - μ)/σ = (-0.40 - 5.00)/2 = -2.70.
Then, use the given table of values to find the probability of a Z value being 2.70 standard deviations below the mean (i.e., when z ≤ 0). The value is 1 - P(Z≤ +2.70).
In this problem, the solution is: 1-0.9965 = 0.0035 = 0.35%.