Consider the normal curve. (Give your answers correct to four decimal places.)
(a) Find the area to the right of z = 0.00.
(b) Find the area to the right of z = 1.1.
(c) Find the area to the right of z = -1.86.
(d) Find the area to the left of z = 1.48.
(e) Find the area to the left of z = -1.48.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for the Z scores.
To find the areas to the right or left of specific z-scores on a normal curve, you can use a standard normal distribution table or a statistical calculator.
(a) To find the area to the right of z = 0.00:
The area to the right of any particular z-score on a normal curve is equal to 1 minus the area to the left of that z-score. Since z = 0.00 is the mean of the standard normal distribution, the area to the left of it is 0.5000. Therefore, the area to the right of z = 0.00 is 1 - 0.5000 = 0.5000.
(b) To find the area to the right of z = 1.1:
Using the standard normal distribution table or calculator, you can find the area to the left of z = 1.1, which is 0.8643. Again, since we want the area to the right, subtracting this value from 1 gives us the desired result: 1 - 0.8643 = 0.1357.
(c) To find the area to the right of z = -1.86:
Using the standard normal distribution table or calculator, you can find the area to the left of z = -1.86, which is 0.0312. Subtracting this value from 1 gives us the area to the right: 1 - 0.0312 = 0.9688.
(d) To find the area to the left of z = 1.48:
Using the standard normal distribution table or calculator, you can directly find the area to the left of z = 1.48, which is 0.9306.
(e) To find the area to the left of z = -1.48:
Like in (d), we can use the standard normal distribution table or calculator to directly find the area to the left of z = -1.48, which is 0.0694.