Waiting times at a doctor office are normally distributed with a mean of 35 minutes, and a standard deviation of 10 minutes. 25% of the patients have to wait less than how many minutes?
To find the answer to this question, we need to use the concept of z-scores, which will enable us to convert raw data into standardized values based on the normal distribution.
First, let's find the z-score corresponding to the given percentage (25%). We can do this by using a standard normal distribution table or a calculator.
Using the standard normal distribution table, we find that the z-score corresponding to the 25th percentile is approximately -0.674.
The formula to calculate the z-score is:
z = (x - μ) / σ
where:
x = raw score
μ = mean
σ = standard deviation
Rearranging the formula to solve for x, we have:
x = (z * σ) + μ
Plugging in the values, we have:
x = (-0.674 * 10) + 35
x = -6.74 + 35
x ≈ 28.26
Therefore, approximately 28.26 minutes is the waiting time at which 25% of the patients have to wait less than.