Question

The U.S. Bureau of Economics Ststistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4246. A Boston worker is randomly selected.

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places)

a.) What is the probability that the worker's annual salary is more than $61,000?

b.) What is the probability that the worker's annual salary is less than $47,000?

c.) What is the probability that the worker's annual salary is more than $39,000?

d.) What is the probability that the worker's annual salary is between $45,000 and $53,000?

Answer 1

Solution :

(a)

P(x > 61000) = 1 - P(x < 61000)

= 1 - P[(x - ) / < (61000 - 50542) / 4246]

= 1 - P(z < 2.46)

= 0.0069

(b)

P(x < 47000) = P[(x - ) / < (47000 - 50542) / 4246]

= P(z < -0.83)

= 0.2033

(c)

P(x > 39000) = 1 - P(x < 39000)

= 1 - P[(x - ) / < (39000 - 50542) / 4246]

= 1 - P(z < -2.72)

= 0.9967

(d)

P(45000 < x < 53000)

= P[(45000 - 50542)/ 4246) < (x - ) /  < (53000 - 50542) / 4246) ]

= P(-1.31 < z < 0.58)

= P(z < 0.58) - P(z < -1.31)

= 0.6239