Answer to Question #225982 in Statistics and Probability for Mustafa Zaidi

Question

Family incomes have a mean of $60 000 with a standard deviation of $20 000. The data is normally distributed. What is the probability of a randomly chosen family having an income greater than $50 000? Provide evidence of your work by typing out your full solution.

ASP

Answer 1

$\mu=60000 \\ \sigma=20000 \\ P(X>50000) = 1-P(X<50000) \\ = 1- P(Z< \frac{50000-60000}{20000}) \\ = 1 -P(Z< -0.5) \\ =1 -0.3085 \\ = 0.6915$