1. To the right of Z=0.5
2. Between Z=0.43 and Z=2.56
3. To the left of Z=-1.29 and to the right of Z=2.05
4. To the left of Z=-0.15
5. Between Z=-1.89 and Z=0
You can play around with Z table stuff at
davidmlane.com/hyperstat/z_table.html
To answer these questions, we need to refer to the standard normal distribution table, also known as the z-table. This table provides the cumulative probabilities for the standard normal distribution.
1. To find the area to the right of Z=0.5, we look up the z-value 0.5 in the z-table. The table gives us the cumulative probability for the left side of the distribution. To find the area to the right, we subtract the cumulative probability from 1. The value we get is the probability of finding a value greater than Z=0.5.
2. To find the area between Z=0.43 and Z=2.56, we find the cumulative probabilities for both Z-values using the z-table. Then we subtract the cumulative probability for Z=0.43 from the cumulative probability for Z=2.56. The result is the probability of finding a value between these two Z-values.
3. To find the area to the left of Z=-1.29 and to the right of Z=2.05, we first find the cumulative probability for each Z-value separately using the z-table. Then, we subtract the cumulative probability for Z=-1.29 from 1 and add it to the cumulative probability for Z=2.05. The result is the probability of finding a value to the left of Z=-1.29 or to the right of Z=2.05.
4. To find the area to the left of Z=-0.15, we look up the z-value -0.15 in the z-table. The table provides the cumulative probability for the left side of the distribution. This cumulative probability represents the area under the curve to the left of Z=-0.15.
5. To find the area between Z=-1.89 and Z=0, we find the cumulative probabilities for both Z-values using the z-table. Then we subtract the cumulative probability for Z=-1.89 from the cumulative probability for Z=0. The result is the probability of finding a value between these two Z-values.
1. To find the area to the right of Z=0.5, we need to calculate the probability that a standard normal random variable is greater than 0.5. This can be done using a standard normal distribution table or a calculator.
2. To find the area between Z=0.43 and Z=2.56, we need to calculate the probability that a standard normal random variable is greater than 0.43 and less than 2.56. This can also be done using a standard normal distribution table or a calculator.
3. To find the area to the left of Z=-1.29 and to the right to Z=2.05, we need to calculate the probability that a standard normal random variable is less than -1.29 and greater than 2.05. This can be done by finding the probability to the left of -1.29 and subtracting it from the probability to the left of 2.05.
4. To find the area to the left of Z=-0.15, we need to calculate the probability that a standard normal random variable is less than -0.15. Again, this can be done using a standard normal distribution table or a calculator.
5. To find the area between Z=-1.89 and Z=0, we need to calculate the probability that a standard normal random variable is greater than -1.89 and less than 0. This can be done using a standard normal distribution table or a calculator.