According to data released by the Chamber of Commerce of a certain city, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 575 and a standard deviation of 50. Find the probability that a female factory worker selected at random from the city makes a weekly wage of $550 to $625.
A) The probability is 0.5438.
B) The probability is 0.5339.
C) The probability is 0.5328.
D) The probability is 0.4297.

Question

According to data released by the Chamber of Commerce of a certain city, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 575 and a standard deviation of 50. Find the probability that a female factory worker selected at random from the city makes a weekly wage of $550 to $625. ​
A) The probability is 0.5438.
B) The probability is 0.5339.
C) The probability is 0.5328.
D) The probability is 0.4297.

Quizplus · Accepted Answer

To find the probability that a female factory worker makes a weekly wage of $550 to $625, we use the properties of the normal distribution. We first convert the wages to z-scores using the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $550, the z-score is $\frac{550 - 575}{50} = -0.5$, and for $625, it is $\frac{625 - 575}{50} = 1$. Looking these z-scores up in the standard normal distribution table or using a calculator, we find the probabilities corresponding to these z-scores and subtract the smaller from the larger to find the probability of a wage between $550 and $625. The correct probability is approximately 0.5328, which corresponds to the cumulative probability from -0.5 to 1 in the standard normal distribution.

According to Data Released by the Chamber of Commerce of a Certain