According to data released by a city's Chamber of Commerce, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 470 and a standard deviation of 40. Find the probability that a female factory worker selected at random from the city has a weekly wage of $450 to $550. Round your answer to four decimal places.
A) 0.103
B) 0.2224
C) 0.3842
D) 0.6687
E) 0.5754

Question

According to data released by a city's Chamber of Commerce, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 470 and a standard deviation of 40. Find the probability that a female factory worker selected at random from the city has a weekly wage of $450 to $550. Round your answer to four decimal places. ​
A) 0.103
B) 0.2224
C) 0.3842
D) 0.6687
E) 0.5754

Quizplus · Accepted Answer

To solve this problem, we need to find the area under the normal distribution curve between the two given values of weekly wages.

First, we need to standardize the values using the formula:

z = (x - μ) / σ

Where: 
x = weekly wage 
μ = mean = 470 
σ = standard deviation = 40

For $450:

z = (450 - 470) / 40 = -0.5

For $550:

z = (550 - 470) / 40 = 2

Next, we use a standard normal distribution table or calculator to find the probabilities for the corresponding z-values.

P(z between -0.5 and 2) = 0.6687

Therefore, the probability that a female factory worker selected at random from the city has a weekly wage of $450 to $550 is 0.6687 or 66.87%, rounded to four decimal places.

According to Data Released by a City's Chamber of Commerce