If Z is a standard normal variable, find the probability that Z lies between -1.10 and -0.36
Use the table of the area under the normal distribution in the back of your statistics textbook to find the area between these Z values and the mean. Since they are both on the negative side of the mean, subtract one area from the other.
I hope this helps. Thanks for asking.
To find the probability that Z lies between -1.10 and -0.36, you need to determine the area under the standard normal distribution curve between these two Z values.
Here's how you can use the table in the back of your statistics textbook to find the area:
1. Locate the Z value closest to -1.10 in the first column of the table. Let's call this value Z1. In this case, Z1 could be -1.1 or the closest value to it that can be found in the table.
2. Locate the Z value closest to -0.36 in the first column of the table. Let's call this value Z2. In this case, Z2 could be -0.4 or the closest value to it that can be found in the table.
3. Look for the corresponding values in the table where the row corresponds to Z1 and the column corresponds to Z2. This will give you the area between Z1 and Z2.
4. Since Z1 and Z2 are both negative values, the area between them represents the probability that Z lies between -1.10 and -0.36.
If the table provides the cumulative probability (area to the left of the Z value), subtract the value corresponding to Z1 from the value corresponding to Z2 to find the area between them.
If the table provides the probability for the entire distribution (cumulative probability (area to the left of the Z value) + 0.5000 (half of the distribution)), subtract the value corresponding to Z1 from the value corresponding to Z2 and then subtract 0.5 * (Z2 - Z1) to find the area between them.
I hope this explanation helps you understand how to utilize the table to find the probability. Let me know if you have any further questions!