Find the area under the standard normal curve to the right of the following z-values. Round your answer to four decimal places.(a) Find the area under the standard normal curve to the right of =z2.38.(b) Find the area under the standard normal curve to the right of =z1.38.(c) Find the area under the standard normal curve to the right of =z0.61.(d) Find the area under the standard normal curve to the right of =z−2.25.
Question
Find the area under the standard normal curve to the right of the following z-values. Round your answer to four decimal places.(a) Find the area under the standard normal curve to the right of =z2.38.(b) Find the area under the standard normal curve to the right of =z1.38.(c) Find the area under the standard normal curve to the right of =z0.61.(d) Find the area under the standard normal curve to the right of =z−2.25.
Solution
To find the area under the standard normal curve to the right of a given z-value, we need to look up the z-value in a standard normal distribution table or use a calculator with a normal distribution function. The table or calculator will give us the area to the left of the z-value, so we subtract that from 1 to get the area to the right.
(a) For z = 2.38, the area to the left is approximately 0.9916. So, the area to the right is 1 - 0.9916 = 0.0084.
(b) For z = 1.38, the area to the left is approximately 0.9162. So, the area to the right is 1 - 0.9162 = 0.0838.
(c) For z = 0.61, the area to the left is approximately 0.7291. So, the area to the right is 1 - 0.7291 = 0.2709.
(d) For z = -2.25, the area to the left is approximately 0.0122. So, the area to the right is 1 - 0.0122 = 0.9878.
So, the areas under the standard normal curve to the right of the given z-values are approximately 0.0084, 0.0838, 0.2709, and 0.9878, respectively.
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