Final answer:
To find the probability that the average salary of 30 randomly selected pharmacy techs is less than $34,200, calculate the z-score using the formula z = (x - μ) / (σ / √n), then use the standard normal distribution table to find the corresponding probability. In this case, the probability is approximately 0.9554 or 95.54%.
Step-by-step explanation:
To find the probability that the average salary of 30 randomly selected pharmacy techs is less than $34,200, we need to calculate the z-score and use the standard normal distribution table.
The formula to calculate the z-score is:
z = (x - μ) / (σ / √n)
Where x is the desired average salary, μ is the mean, σ is the standard deviation, and n is the number of pharmacy techs selected.
In this case, x = $34,200, μ = $33,000, σ = $4,000, and n = 30.
Plugging in the values, we get:
z = ($34,200 - $33,000) / ($4,000 / √30)
Simplifying, we find:
z ≈ 1.69
Using the standard normal distribution table, we can find that the probability of z < 1.69 is approximately 0.9554.
So the probability that the average salary of 30 randomly selected pharmacy techs is less than $34,200 is approximately 0.9554 or 95.54%.