Question

Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $300 and $350. What is the percentage?

A. 7.5%
B. 15%
C. 10%
D. 2.5%

Answer 1

To find the probability that a worker makes between $300 and $350, calculate the z-scores and find the area between them on the normal distribution curve.

Step-by-step explanation:

To find the probability that a worker selected at random makes between $300 and $350, we need to calculate the z-scores for each of these values using the formula:

z = (x - μ) / σ

Where x is the value, μ is the mean, and σ is the standard deviation.

For $300:
z = (300 - 400) / 50 = -2
For $350:
z = (350 - 400) / 50 = -1

Next, we need to find the area under the normal distribution curve between these two z-scores using a standard normal distribution table or a calculator. The area between -2 and -1 is approximately 0.1587.

So, the probability that a worker selected at random makes between $300 and $350 is 0.1587, or 15.87%.