Find the area under the standard normal distribution curve for the following z-values:
a. Between z= 0 and z = 2.01
b. Between z = 0 and z = -0.32
c. To the left of z = -0.73
d. To the right of z = 0.32
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to your Z scores.
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a. To find the area between z=0 and z=2.01, we need to find the probability that a standard normal random variable takes on a value between 0 and 2.01.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = 2.01 is approximately 0.9803.
The area between z = 0 and z = 2.01 can be calculated by subtracting the area to the left of z = 0 from the area to the left of z = 2.01:
Area between z = 0 and z = 2.01 = Area to the left of z = 2.01 - Area to the left of z = 0
= 0.9803 - 0.5
= 0.4803
Therefore, the area under the standard normal distribution curve between z = 0 and z = 2.01 is approximately 0.4803.
b. To find the area between z = 0 and z = -0.32, we need to find the probability that a standard normal random variable takes on a value between 0 and -0.32.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = -0.32 is approximately 0.3751.
The area between z = 0 and z = -0.32 can be calculated by subtracting the area to the left of z = -0.32 from the area to the left of z = 0:
Area between z = 0 and z = -0.32 = Area to the left of z = 0 - Area to the left of z = -0.32
= 0.5 - 0.3751
= 0.1249
Therefore, the area under the standard normal distribution curve between z = 0 and z = -0.32 is approximately 0.1249.
c. To find the area to the left of z = -0.73, we need to find the probability that a standard normal random variable takes on a value less than -0.73.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = -0.73 is approximately 0.2327.
Therefore, the area under the standard normal distribution curve to the left of z = -0.73 is approximately 0.2327.
d. To find the area to the right of z = 0.32, we need to find the probability that a standard normal random variable takes on a value greater than 0.32.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = 0.32 is approximately 0.6255.
Therefore, the area under the standard normal distribution curve to the right of z = 0.32 is approximately 1 - 0.6255 = 0.3745.
To find the area under the standard normal distribution curve, you can use a standard normal distribution table or a statistical calculator.
a. To find the area between z = 0 and z = 2.01, you need to find the area to the left of z = 2.01 and subtract the area to the left of z = 0. Using a standard normal distribution table or calculator, you can determine the area to the left of z = 2.01 is approximately 0.9778 and the area to the left of z = 0 is 0.5000. Therefore, the area between z = 0 and z = 2.01 is approximately 0.9778 - 0.5000 = 0.4778.
b. To find the area between z = 0 and z = -0.32, you can again find the area to the left of each z-value and then subtract. Using a standard normal distribution table or calculator, you can determine the area to the left of z = -0.32 is approximately 0.3745, and the area to the left of z = 0 is 0.5000. Subtracting, you get 0.5000 - 0.3745 = 0.1255 for the area between z = 0 and z = -0.32.
c. To find the area to the left of z = -0.73, you can use a standard normal distribution table or calculator. The area to the left of z = -0.73 is approximately 0.2336.
d. To find the area to the right of z = 0.32, you can use a standard normal distribution table or calculator. The area to the left of z = 0.32 is approximately 0.6255. To find the area to the right, subtract the area to the left from 1: 1 - 0.6255 = 0.3745. The area to the right of z = 0.32 is approximately 0.3745.
Remember, these values are approximations, as the area under the standard normal distribution curve is ideally infinite.