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 (Q1 and Q3) for the class, we can use Z-scores along with the mean and standard deviation provided.

The Z-score formula is given by:
Z = (X - μ) / σ

Where:
- Z is the Z-score
- X is the value we want to convert to a Z-score
- μ is the population mean
- σ is the standard deviation

To find the quartiles, we need to find the corresponding Z-scores for the desired probabilities (P), which in this case are P(Z < 0.25) and P(Z < 0.75).

1. To find the first quartile (Q1):
- We want to find the Z-score that corresponds to P(Z < 0.25).
- Using a Z-table or a calculator, we can find that the Z-score corresponding to P(Z < 0.25) is approximately -0.674.
- Now we can rearrange the Z-score formula to solve for X:
X = Z * σ + μ
- Plugging in the known values:
X = (-0.674) * 3.03 + 21.9
- Calculating the result:
X ≈ 19.74
- So, the first quartile (Q1) for the class is approximately 19.74.

2. To find the third quartile (Q3):
- We want to find the Z-score that corresponds to P(Z < 0.75).
- Using a Z-table or a calculator, we can find that the Z-score corresponding to P(Z < 0.75) is approximately 0.674.
- Again, rearranging the Z-score formula to solve for X:
X = Z * σ + μ
- Plugging in the known values:
X = (0.674) * 3.03 + 21.9
- Calculating the result:
X ≈ 23.06
- So, the third quartile (Q3) for the class is approximately 23.06.

By using the Z-score formula and the provided mean and standard deviation, we were able to calculate the approximate values of Q1 and Q3 for the class ages.