Question
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?
What is the 25th percentile of this distribution?
Answers
GPT 3.5
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.
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.