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 quartile (Q1) and third quartile (Q3) using the given information about mean and standard deviation, you will need to use the Z-score formula and the properties of the standard normal distribution.
First, recall that the standard normal distribution has a mean of 0 and a standard deviation of 1.
The formula to convert a value (X) from a normal distribution to a Z-score is:
Z = (X - μ) / σ
Here, μ represents the mean and σ represents the standard deviation.
To find the first quartile (Q1), you need to find the value of X that corresponds to a Z-score such that P(Z < Z-score) = 0.25 (25th percentile). In other words, you want to find the X value such that 25% of the data lies to the left of it.
Using the Z-score formula, you can rewrite it as:
Z-score = (X - μ) / σ
Rearranging it to solve for X:
X = Z-score * σ + μ
Substituting the given values:
Z-score = -0.674 (since P(Z < -0.674) = 0.25, you can look up this value in a standard normal distribution table)
X = -0.674 * 3.03 + 21.9 = 19.137
Therefore, the first quartile (Q1) for the class age would be 19.137.
Similarly, to find the third quartile (Q3), you need to find the X value that corresponds to a Z-score such that P(Z < Z-score) = 0.75 (75th percentile). In other words, you want to find the X value such that 75% of the data lies to the left of it.
Using the Z-score formula and following the same steps as above, you can find the X value for the third quartile (Q3).
Z-score = 0.674 (since P(Z < 0.674) = 0.75, you can look up this value in a standard normal distribution table)
X = 0.674 * 3.03 + 21.9 = 23.588
Therefore, the third quartile (Q3) for the class age would be 23.588.
Remember, this method assumes that the age distribution follows a normal distribution, which may not always be the case in practice.