Question

For standard normal random variable Z, given p(Z < z0) = 0.33, find z0-score.

Answer 1

To find the z0-score for P(Z < z0) = 0.33 in a standard normal distribution, you can use a z-table or a calculator command invNorm(0.33,0,1) to find that z0 is approximately -0.44.

Step-by-step explanation:

To find the z0-score when the probability P(Z < z0) equals 0.33, we can use a standard normal probability table or a calculator with statistical functions. We are looking for the z-score that corresponds to the area of 0.33 to the left of the z-score under the standard normal curve.

The standard normal distribution, Z~N(0,1), has a mean of 0 and a standard deviation of 1.

Using the z-table or a calculator with the command invNorm(0.33,0,1), we can find the value of z0.

The z-score that corresponds to a cumulative area of 0.33 is approximately -0.44. This means that z0 is -0.44, indicating that the value is 0.44 standard deviations below the mean.