Use the z-table to find the requested probabilities. Enter your answers to 4 decimal places.
(a)
P(z < −1.02) =
Incorrect: Your answer is incorrect.
(b)
P(z ≥ 2.43) =
(c)
P(−1.80 < z < 1.36) =
How can the answer be incorrect, if there is no answer?
Using the Z table in the back of your statistics text labeled something like "areas under normal distribution," use the smaller proportion for a and b.
For c, add proportions between Z scores and mean.
To use the z-table to find the requested probabilities, you need to follow these steps:
Step 1: Identify the given z-value.
In this case, we have the following z-values:
(a) z = -1.02
(b) z = 2.43
(c) z1 = -1.80 and z2 = 1.36
Step 2: Locate the z-values in the z-table.
The z-table provides the cumulative probability values for different z-values. It tells you the area under the normal distribution curve to the left of a given z-value.
Step 3: Find the probability using the z-table.
(a) To find P(z < -1.02), locate -1.0 on the left-hand side of the table and go to the second decimal place (0.02). The value in the table is 0.8461. Therefore, the probability is 0.8461.
(b) To find P(z ≥ 2.43), locate 2.4 on the left-hand side of the table and go to the third decimal place (0.03). The value in the table is 0.9925. To find the probability of z being greater than or equal to 2.43, subtract the value from 1. So, the probability is 1 - 0.9925 = 0.0075.
(c) To find P(-1.80 < z < 1.36), locate -1.8 on the left-hand side of the table and go to the first decimal place (0.08). The value in the table is 0.0359. Then, locate 1.3 on the left-hand side of the table and go to the second decimal place (0.06). The value in the table is 0.9032. Subtract the probability for -1.8 (0.0359) from the probability for 1.3 (0.9032) to find the probability between the two values. So, the required probability is 0.9032 - 0.0359 = 0.8673.
Therefore, the answers to the given probabilities are:
(a) P(z < -1.02) = 0.8461
(b) P(z ≥ 2.43) = 0.0075
(c) P(-1.80 < z < 1.36) = 0.8673