Find the indicated probability given that Z is a random variable with a standard normal distribution. (Round your answer to four decimal places.)
P(0 ≤ Z ≤ 0.33)
To find the indicated probability P(0 ≤ Z ≤ 0.33) given that Z is a random variable with a standard normal distribution, we need to use standard normal distribution tables or a calculator that can provide us with the cumulative probability.
Here are the steps to find the probability using a standard normal distribution table:
1. Locate the z-score of the lower bound 0 in the table. The z-score of 0 corresponds to the mean of the distribution.
- The cumulative probability for a z-score of 0 is 0.5000.
2. Locate the z-score of the upper bound 0.33 in the table.
- The cumulative probability for a z-score of 0.33 is 0.6293.
3. Calculate the difference between the cumulative probabilities: 0.6293 - 0.5000 = 0.1293.
Therefore, the indicated probability P(0 ≤ Z ≤ 0.33) is approximately 0.1293 (rounded to four decimal places).
You can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html