Answer:
The probability is 0.9973 or 99.73%
Step-by-step explanation:
* Lets explain how to solve the problem
- For the probability that a < X < b (X is between two numbers, a and b),
convert a and b into z-scores and use the table to find the area
between the two z-values.
- Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- For certain workers, the mean wage is $5.00/hr, with a standard
deviation of $0.25
∴ μ = 5 and σ = 0.25
- The worker wage is between $4.25 and $5.75
∴ 4.25 < X < 5.75
∵ z = (x - μ)/σ
∴ z = (4.25 - 5)/0.25 = -0.75/0.25 = -3
∴ z = (5.75 - 5)/0.25 = 0.75/0.25 = 3
- Use the z table to find the corresponding area
∵ P(z > -3) = 0.00135
∵ P(z < 3) = 0.99865
∴ P(-3 < z < -2) = 0.99865 - 0.00135 = 0.9973
∵ P(4.25 < X < 5.75) = P(-3 < z < 3)
∴ P(4.25 < X < 5.75) = 0.9973 = 99.7%
* The probability is 0.9973 or 99.73%
