DIAGRAMS MUST BE DRAWN

Given the standard normal distribution, determine:Prob Z greater than 1.50
Prob Z between1.06 and 1.96
Given the standard normal distribution determine
the Z values that contain 80% in the middle of the curve.

You need to draw a normal curve. Label 1.50 and shade in everything from 1.50 to the right under the tail You can look up this value on a calculator or from a Z-table. Be careful because Z-tables may give you only the lower tail.

For 1.06 to 1.96, Again draw the curve and label the two values. (Remember the middle of the curve is "o". Color between these two numbers. Again, this can be done on a calculator, like the TI-83 or use the x-table.

80% in the middle means there is 10% on each side of the middle. If I remember correctly, to have 10% in each tail, the z-value will be -1.645, 1.645. Check a table to be sure.

To determine the probabilities and Z values for the given scenarios, we need to use the standard normal distribution table or a statistical software.

1. Probability of Z greater than 1.50:
To find the probability of Z greater than 1.50, we need to find the area under the standard normal curve to the right of 1.50.

Method 1: Using a standard normal distribution table:
Look up the value of 1.50 in the table. The table will give you the cumulative probability associated with that Z value. Subtract the cumulative probability from 1 to find the probability of Z greater than 1.50.

Method 2: Using a statistical software:
You can use a statistical software such as Excel, SPSS, or an online calculator to calculate this probability directly. By inputting the value of 1.50, the software will give you the probability of Z greater than 1.50.

2. Probability of Z between 1.06 and 1.96:
To find the probability of Z values between 1.06 and 1.96, we need to find the area under the standard normal curve between these two Z values.

Method 1: Using a standard normal distribution table:
Look up the values of 1.06 and 1.96 separately in the table. The table will give you the cumulative probabilities associated with these Z values. Subtract the cumulative probability of 1.06 from the cumulative probability of 1.96 to find the probability of Z between 1.06 and 1.96.

Method 2: Using a statistical software:
Input the values of 1.06 and 1.96 into a statistical software, and it will give you the probability of Z between these two values.

3. Z values containing 80% in the middle of the curve:
To find the Z values that contain 80% in the middle of the curve, we need to find the two Z values for which the area under the standard normal curve between them is 80%.

Method 1: Using a standard normal distribution table:
Look for the cumulative probability in the table closest to 0.40 (half of 0.80). Find the corresponding Z value. Subtract this Z value from 0 to find the other Z value.

Method 2: Using a statistical software:
Using a statistical software, input the cumulative probability of 0.40 (either as 0.40 or 0.80/2) to find the corresponding Z value. Subtract this Z value from 0 to find the other Z value.