Question

Calculate the probability for the following problems (Please keep 4 decimal places). 1. P(z>2.33)= 2. P(z<−2.61)= 3. P(−2.16

Answer 1

To calculate the probability, use the standard normal distribution table (z-table). For P(z>2.33), find the area to the left of 2.33 and subtract from 1. For P(z<-2.61), find the area to the left of -2.61. For P(-2.16

Step-by-step explanation:

To calculate the probability, we use the standard normal distribution table, also known as the z-table. The z-table provides the area under the normal curve to the left of a given z-score. In this case, we are given specific z-scores and we need to find the corresponding probabilities.

1. P(z > 2.33): From the z-table, we find the area to the left of 2.33 is 0.9900. To find the area to the right, we subtract this value from 1: 1 - 0.9900 = 0.0100.
2. P(z < -2.61): From the z-table, we find the area to the left of -2.61 is 0.0047.
3. P(-2.16 < z < 1.92): We first find the area to the left of -2.16, which is 0.0158. Then we find the area to the left of 1.92, which is 0.9732. To find the area between these two z-scores, we subtract the smaller area from the larger area: 0.9732 - 0.0158 = 0.9574.