The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.
A. About $46.30
B. About $43.30
C. About $43.40
D. about $43.20
I came up with $43.26 which its not a choice. Please help!!
To find the 25th percentile of a normally distributed variable, you can use the z-score formula:
z = (X - μ) / σ
Where:
X is the value you want to find the percentile for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
In this case, X represents the 25th percentile, the mean (μ) is $50, and the standard deviation (σ) is $10.
To find the corresponding z-score for the 25th percentile, you can use a standard normal distribution table or a calculator. The z-score for the 25th percentile is approximately -0.6745.
Now, we can rearrange the z-score formula to solve for X:
X = μ + (z * σ)
Plugging in the known values:
X = $50 + (-0.6745 * $10)
X ≈ $50 - $6.745
X ≈ $43.26
So, you are correct that the value for the 25th percentile is approximately $43.26, which is not one of the answer choices provided. It seems there may be a discrepancy in the given answer choices.