Question

In: Statistics and Probability

Assume that 40% of graduates come from University A and and earn salaries of 30,000 on...

Assume that 40% of graduates come from University A and and earn salaries of 30,000 on average with a standard deviation of 5,000. The remainder come from University B and earn salaries of 25,000 on average with a standard deviation of 7,500. If you are told that a graduate is earning less than 35,000, what is the probability that they came from University A? (Assume salaries are normally distributed.)

Expert Solution

P(z<Z) table :

P(universitiy A) = 0.40

P(universitiy B) = 0.60

P(salary <= 35000 | universitiy A) :

P(salary <= 35000 | universitiy A) = 0.8413

P(salary <= 35000 | universitiy B) :

P(salary <= 35000 | universitiy B) = 0.9088

P(salary <= 35000) = P(salary <= 35000 | universitiy A)*P(universitiy A) + P(salary <= 35000 | universitiy B)*P(universitiy B)

= 0.8413*0.40 + 0.9088*0.60

= 0.8818

P(university A | salary <= 35000) = P(salary <= 35000 | universitiy A)*P(universitiy A) / P(salary <= 35000)

= 0.8413*0.40 / 0.8818

= 0.3816

P(university A | salary <= 35000) = 0.3816

(please UPVOTE)

orchestra answered 1 year ago

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