There is a normal distribution with a mean of 36.9 and standard deviation of 13.9
What is the 25th percentile of this distribution?
To find the 25th percentile, we need to compute the z-score corresponding to this percentile and then convert it back to the original data scale.
The z-score can be found using the z-score formula:
z = (x - μ) / σ
where x is the desired percentile, μ is the mean, and σ is the standard deviation.
Substituting the values into the formula:
z = (x - 36.9) / 13.9
To find the z-score corresponding to the 25th percentile, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution.
Using either method, we find that the z-score corresponding to the 25th percentile is approximately -0.6745.
Now, we can rearrange the z-score formula to solve for x:
x = z * σ + μ
Plugging in the values:
x = -0.6745 * 13.9 + 36.9
Calculating this expression:
x ≈ 27.42
Therefore, the 25th percentile of this normal distribution is approximately 27.42.