1. The natural log of income has a normal distribution with mean 10.35 and variance 2.5. What is the probability that a person has income below $10,000? [
Answers
Given : The natural log of income has a normal distribution with mean 10.35 and variance 2.5
To Find : probability that a person has income below $10,000
Solution:
Natural log of 10000
ln (10000) = 9.21
Value = 9.21
Mean = 10.35
variance 2.5 => SD = √2.5 = 1.58
Z score = ( Value - Mean ) / SD
=> Z score = ( 9.21 - 10.35 ) / 1.58
=> Z score = ( -1.14 ) / 1.58
=> Z score = -0.7215 => 0.235
probability that a person has income below $10,000 = 0.235
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