![standard normal table to the right standard normal table to the right](https://media.cheggcdn.com/media%2Fc16%2Fc1604c43-220b-4877-95d1-0f66cfb4b1c5%2FphpQRtU9z.png)
To make this easier, first draw a picture. The same table will be used, but you will search the center of the table to find the probability first, and then determine the z-score that corresponds to that probability. Starting with a probability, you will find a corresponding z-score. Thus, P (X > 39) ≈ 1 − 0.3085 = 0.6915ĥ.3 Normal Distributions: Finding Values Now the process from 5.2 will be reversed. We need the area to the right of the z-score. For P (X > 54), the area to the right is needed. The mean is µ = 45 and standard deviation is σ = 12. OR, using complements and the answer to part a, P (X ≤ 70) = 1 − P (X > 70) ≈ 1 − 0.1949 ≈ 0.8051 (b) What is the probability that a randomly selected vehicle is traveling under 50 miles per hour? We are interested in P (X 54). We are interested in P (X ≤ 70), thus the area to the left of this z-score can be read directly off the table: 0.8051. Since we are interested in X > 70, we need the area to the right of the z-score, thus P (X > 70) ≈ 1 − 0.8051 ≈ 0.1949 (a) What is the probability that a randomly selected vehicle is not violating the speed limit? The z-score is the same: 0.86. The area corresponding to a z-score of 0.86 in the table is 0.8051. Step 2: Find the appropriate area between the normal curve and the axis using the table: The table contains cumulative areas (to the left of the z-value).
![standard normal table to the right standard normal table to the right](https://www.statext.com/tables/Z-Table(0-Z).jpg)
Chapter 5: Normal Probability Distributions - Solutions Note: All areas and z-scores are approximate.