Question

According to the data released by the Chamber of Commerce of a certain city, the weekly wages of factory workers are normally distributed with a mean of $720 and standard deviation of $40. Find the probability that a worker selected at random from the city makes the following weekly wage. (Round your answers to four decimal places.)

Answer 1

Complete question :

a. Of less than$720?

b. Of more than $840?

c. Between $680 and $760?

Answer:

0.500 ; 0.0013 ; 0.6827

Explanation:

Given that :

Mean, μ = 720

Standard deviation, σ = 40

P(Z < x)

x = (x < 720)

Obtain the standardized value of x

P(x < 720) = (x - μ) / σ

P(x < 720) = (720 - 720) / 40

P(x < 720) = 0

P(Z < 0) = 0.5

B.) More than $840

P(x > 840)

P(x > 840) = (x - μ) / σ

P(x > 840) = (840 - 720) / 40

P(x > 840) = 120 / 40 = 3

P(Z > 3) = 0.0013499 (Z probability calculator)

c. Between $680 and $760?

P(760 < x < 680)

P(760 < x < 680) = ((x - μ) / σ) - ((x - μ) / σ)

P(760 < x < 680) = ((760 - 720) / 40) - (680 - 720) / 40)) = P( Z < - 1) - P(Z < - 1)

P(680 < x < 760) = 0.84134 - 0.15866 = 0.68268