6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
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Find the z-score such that (Z < z).
A
0.34
B
0.75
C
0.62
D
0.66
Verified step by step guidance1
Understand that the problem is asking for a z-score corresponding to a given probability in a standard normal distribution. The probability given is P(Z < z) = 0.6331.
Recall that the z-score is a measure of how many standard deviations an element is from the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
Use a standard normal distribution table (z-table) or a statistical software to find the z-score that corresponds to the cumulative probability of 0.6331.
Locate the probability value 0.6331 in the z-table. The z-table lists cumulative probabilities for z-scores, so you need to find the closest value to 0.6331.
Once you find the closest probability value in the z-table, identify the corresponding z-score. This z-score is the solution to the problem.
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