Multiple Choice
Assume is normally distributed with a mean of and a standard deviation of . What is the z-score for ?
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
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Find the area of the shaded region under the standard normal distribution.
A
0.7881
B
0.7119
C
0.2119
D
0.2881
Verified step by step guidance1
Identify the shaded region on the standard normal distribution curve. The shaded area is between the z-scores of 0 and 0.8.
Understand that the standard normal distribution is symmetric around the mean, which is 0, and has a standard deviation of 1.
Use the standard normal distribution table (z-table) to find the area to the left of the z-score 0.8. This value represents the cumulative probability from the left up to 0.8.
Find the area to the left of the z-score 0, which is 0.5, since the mean of the standard normal distribution is 0.
Subtract the area to the left of z = 0 from the area to the left of z = 0.8 to find the area of the shaded region. This will give you the probability of the z-score being between 0 and 0.8.
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