Respuesta :
Answer:
Step-by-step explanation:
To find the probability that a worker selected at random makes between $400 and $550, we need to calculate the z-scores for both values and then use the z-table to find the probabilities.
Given:
Mean (μ) = $400
Standard deviation (σ) = $50
Calculate the z-scores for $400 and $550: For $400: [ z = \frac{X - \mu}{\sigma} = \frac{400 - 400}{50} = 0 ]
For $550: [ z = \frac{X - \mu}{\sigma} = \frac{550 - 400}{50} = 3 ]
Using the 68% - 95% - 99.7% rule:
The area between the mean and one standard deviation (z = 1) is approximately 68%.
The area between the mean and two standard deviations (z = 2) is approximately 95%.
The area between the mean and three standard deviations (z = 3) is approximately 99.7%.
Calculate the probability that a worker's wage is between $400 and $550:
Since $550 corresponds to z = 3, the area to the left of z = 3 is approximately 99.7%.
Since $400 corresponds to z = 0, the area to the left of z = 0 is 0.5 (50%).
Therefore, the probability that a worker makes between $400 and $550 is: [ P(400 < w < 550) = P(z < 3) - P(z < 0) = 0.997 - 0.5 = 0.497 ]
Therefore, the probability that a worker selected at random makes between $400 and $550 is approximately 49.7%.
