Scores on an english test are normally distributed with a mean of 33.6 and a standard deviation of 8.3. Find the 41st percentile?
Go to the Z tables for standard normal distrobution and find the normalized value for 0.41. You have to interpralte because the closest value is between -0.22 and -0.23. So Z=approx-0.225. From here you can solve for x using algebra. (x-33.6)/8.3=-0.225. Therefore x=(-0.225*8.3)+33.6=31.7325
Well, you could say that the 41st percentile is a pretty lukewarm score. It means that around 41% of the students did worse than you, which could be comforting or terrifying depending on your perspective. But don't worry, you're not alone in the middle! Remember, percentiles are just a way to measure how you compare to others. So if you score at the 41st percentile, you're simply right in the middle of the pack, not too shabby!
To find the 41st percentile, we need to find the value that separates the bottom 41% from the top 59% of the distribution.
Step 1: Convert the percentile to a z-score using the z-table or a statistical calculator. The z-score represents the number of standard deviations an individual score is from the mean.
The 41st percentile corresponds to a cumulative probability of 0.41. Let's find the z-score for this probability.
Step 2: Use the z-score formula to find the z-score:
Z = (x - μ) / σ
Where:
Z is the z-score,
x is the value we need to find (unknown),
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
Substituting the given values, we have:
Z = (x - 33.6) / 8.3
Step 3: Determine the z-score that corresponds to the 41st percentile. We can use a z-table or a statistical calculator to find this value.
Using the z-table, we find that the z-score corresponding to a cumulative probability of 0.41 is approximately -0.27.
Step 4: Solve the equation for x to find the value at the 41st percentile:
-0.27 = (x - 33.6) / 8.3
Multiply both sides by 8.3:
-2.241 = x - 33.6
Add 33.6 to both sides:
x = 33.6 - 2.241
x ≈ 31.359
Therefore, the score at the 41st percentile is approximately 31.359.
To find the 41st percentile in a normally distributed data set, you can use the z-score formula. The z-score measures the number of standard deviations a particular value is from the mean.
The formula for the z-score is:
z = (X - μ) / σ
Where:
X = the value you want to find the percentile for
μ = the mean of the data set
σ = the standard deviation of the data set
In this case, you want to find the value (the score on the test) corresponding to the 41st percentile. To do this, we need to find the z-score that corresponds to the 41st percentile.
The percentile can be converted to a z-score by using the standard normal distribution table or a statistical calculator.
Step 1: Convert the percentile to a decimal.
41st percentile = 41 / 100 = 0.41
Step 2: Find the z-score using the standard normal distribution table or a calculator.
From the table or calculator, you will find that the z-score corresponding to the 41st percentile is approximately -0.27.
Step 3: Plug the values into the z-score formula and solve for X:
z = (X - μ) / σ
-0.27 = (X - 33.6) / 8.3
Now, solve for X.
-0.27 * 8.3 = X - 33.6
-2.241 = X - 33.6
X = -2.241 + 33.6
X = 31.359
Therefore, the score at the 41st percentile is approximately 31.359.