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 $600 and a standard deviation of $50. What is the probability that a worker selected at random from the city makes a weekly wage of more than $755.
A) The probability is 0.0074.
B) The probability is 0.6761.
C) The probability is 0.0010.
D) The probability is 0.0068.

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 $600 and a standard deviation of $50. What is the probability that a worker selected at random from the city makes a weekly wage of more than $755. ​
A) The probability is 0.0074.
B) The probability is 0.6761.
C) The probability is 0.0010.
D) The probability is 0.0068.

Quizplus · Accepted Answer

To solve this problem, we need to use the standard normal distribution. We first transform the original distribution with a mean of $600 and a standard deviation of $50 into a standard normal distribution with a mean of 0 and a standard deviation of 1:

z = (x - mu) / sigma = (755 - 600) / 50 = 3.1

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.1 or higher is approximately 0.0010. Therefore, the probability that a worker selected at random from the city makes a weekly wage of more than $755 is 0.0010 or 0.1%.

According to the Data Released by the Chamber of Commerce