In our initial survey, the guess at the mean age for the class had a mean of 21.9 and a standard deviation 3.03.
Using this information, what would be the first and third quartile be for the class? ( P(Z<.25) and P(Z<.75) respectively)
I think you use the Z score formula to find the "X" values or construct an assemblage of data points to find the min, max, med, and Q1 and Q3? i've been stuck on how to solve it for day's.. i just don't get it. thank you for your feedback
To find the first and third quartiles based on the given mean and standard deviation, you will need to convert the quartiles into Z-scores and then use these Z-scores to find the corresponding values.
First, let's calculate the Z-scores for the first and third quartiles using the following formula:
Z = (X - μ) / σ
where:
- Z represents the Z-score
- X represents the value you want to find the Z-score for
- μ represents the mean
- σ represents the standard deviation
For the first quartile (Q1), we need to find the Z-score for P(Z < 0.25). Using a Z-score table or a standard normal distribution calculator, we can find that the Z-score for P(Z < 0.25) is approximately -0.675.
Using the Z-score formula, we can solve for X (the first quartile value):
-0.675 = (X - 21.9) / 3.03
Solving this equation for X, we get:
X = -0.675 * 3.03 + 21.9 ≈ 19.926
So, the first quartile (Q1) would be approximately 19.926.
Similarly, for the third quartile (Q3), we need to find the Z-score for P(Z < 0.75). Using a Z-score table or a standard normal distribution calculator, we can determine that the Z-score for P(Z < 0.75) is approximately 0.674.
Using the Z-score formula like before:
0.674 = (X - 21.9) / 3.03
Solving for X, we have:
X = 0.674 * 3.03 + 21.9 ≈ 23.893
So, the third quartile (Q3) would be approximately 23.893.
To summarize, the first quartile (Q1) is approximately 19.926 and the third quartile (Q3) is approximately 23.893, based on the provided mean and standard deviation.