Question

1. The annual income of single individuals in Canada is normally distributed with mean $45,000 and standard deviation $10,000.

a. [1] What is the z-score of an annual income of $60,000?

b. [2] What proportion of people have an annual income of at least $60,000?Illustrate your calculations. Annual Income Standard Normal Distribution

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Answer 1

Given that the annual income of single individuals in Canada is normally distributed with mean = $45,000 and a standard deviation of   = $10,000.

a) The Z score is calculated as:

b) The proportion of people have an annual income of at least $60,000 is P(X>=$ 60,000) is calculated by finding the Z score which is calculated above as:

Hence the proportion P(X>=$ 60,000) =P(Z>1.5) is calculated using excel formula for normal distribution which is =1-NORM.S.DIST(1.5,TRUE), hence the proportion is computed as 0.0668.