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 using the given information, you need to understand the concept of the standard normal distribution and how it relates to the quartiles.
The standard normal distribution is a bell-shaped distribution with a mean of 0 and a standard deviation of 1. By converting any value from a normal distribution into a standard normal distribution using the Z-score formula, you can find the corresponding percentile or probability.
Here's how you can find the first and third quartiles:
1. Convert the desired percentiles (25% and 75%) into Z-scores using the formula:
Z = (X - μ) / σ
where X is the value you want to convert, μ is the mean, and σ is the standard deviation.
2. Once you have the Z-scores, you can use a standard normal distribution table or a calculator to find the corresponding probabilities. The table provides the area under the curve to the left of a given Z-score.
3. For the first quartile, you want to find P(Z < 0.25). Look up the Z-score for 0.25 in the standard normal distribution table and find the corresponding probability. This will give you the area to the left of the first quartile.
4. For the third quartile, find P(Z < 0.75) using the same process as above. This will give you the area to the left of the third quartile.
5. Finally, convert the probabilities back to X-values using the Z-score formula and the given mean and standard deviation. The X-values will represent the first and third quartiles for the class.
Remember, the Z-score formula requires a mean and a standard deviation, so make sure you have those values before proceeding. In your case, the mean is given as 21.9 and the standard deviation is given as 3.03.
I hope this explanation helps clarify how to find the first and third quartiles using the Z-score formula and the standard normal distribution.