The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75?
To find the probability that a worker earns more than $6.75, we need to calculate the area under the normal curve to the right of $6.75.
First, we calculate the z-score for $6.75:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, x = $6.75, μ = $6.50, and σ = $0.45.
z = ($6.75 - $6.50) / $0.45
z = $0.25 / $0.45
z ≈ 0.56
Now, we need to find the probability that a worker earns more than $6.75, which is equivalent to finding the probability of getting a z-score greater than 0.56.
Using a z-table or a calculator, we can find that the probability of getting a z-score greater than 0.56 is approximately 0.2881.
Therefore, the probability that a worker at this fast food restaurant earns more than $6.75 is approximately 0.2881, or 28.81%.