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!!
I used my favourite stats calculator
http://davidmlane.com/hyperstat/z_table.html
set it to
"value from an area"
and entered the following data
area = .25
mean = 50
SD = 10
and clicked on "below" to get
43.258 , which you also got, I would say we are correct
Try choosing B
43.258 rounded to one decimal place would be
43.3 , but they should not have placed that zero at the end.
To find the 25th percentile of a normally distributed data with a mean of $50 and a standard deviation of $10, you can use the z-score formula.
The z-score formula is given by:
z = (x - μ) / σ
Where:
x = the value for which you want to find the percentile
μ = the mean of the data
σ = the standard deviation of the data
In this case, you want to find the 25th percentile, which means you are looking for the value x such that 25% of the data falls below it.
To find the z-score for the 25th percentile, you can use a standard normal distribution table or calculate it using the following equation:
z = invNorm(0.25)
Using a calculator or a statistics software, you can find that z ≈ -0.6745.
Now you can solve for x using the z-score formula:
-0.6745 = (x - 50) / 10
Rearranging the equation to solve for x:
-0.6745 * 10 = x - 50
-6.745 = x - 50
x = -6.745 + 50
x ≈ 43.255
Rounding to two decimal places, the 25th percentile of Jen's monthly phone bill is approximately $43.26.
Since none of the given answer choices match exactly, it seems there might be a rounding error or a slight discrepancy in the answer choices. Based on the closest match, the closest answer choice to $43.26 would be option D, which states "about $43.20".
To find the 25th percentile of Jen's monthly phone bill, you can use the formula for z-score and standard deviation. The z-score represents how many standard deviations an observation is away from the mean.
First, calculate the z-score for the 25th percentile using the formula:
z = (x - μ) / σ
where z is the z-score, x is the desired percentile (25th percentile in this case), μ is the mean, and σ is the standard deviation.
Substituting the given values:
z = (x - 50) / 10
To find the value of x, rearrange the equation:
x = z * 10 + 50
Now, we want to find the value of x that corresponds to a z-score of -0.6745, which is the z-score associated with the 25th percentile.
x = -0.6745 * 10 + 50
x = -6.745 + 50
x = 43.255
Rounding to two decimal places, the 25th percentile of Jen's monthly phone bill is approximately $43.26.
Unfortunately, none of the given answer choices match $43.26 exactly. However, based on the given choices, the closest option would be D. about $43.20.