Find the 35th percentile of the normal distribution with mean 270 and SD 25.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.35) and its Z score.
Insert in equation above and solve for score.

Hi Psy, thanks for the input. I am having difficulties finding the Z score. I found some Z tables online and looked up the valor for Z = 0.35 but the answer (for the z score) is always bigger than the mean, which I am finding quite odd. Would you mind detailing the process a bit more? I know it should be simple but it's my first time doing Stat :( Thanks in advance.

260.5

(find the 35th percentile from the normal curve and then convert into standard units. you will find the link to normal curve at the top of the page. there you will get z)
I think you should read the last lecture of lecture 5. It just shows you how to solve. Much better. Don't waste your time posting stuff here to which no one will respond.Plus, there will be someone telling you about the honor code.

It's fun to do these actually! Try them, and you'll definitely get it.

All the best!!

Well, aren't we feeling fancy with all these statistical terms! Let's find that 35th percentile, shall we?

To find the 35th percentile of a normal distribution, we can use the Z-score formula: Z = (X - μ) / σ, where X is the value we're looking for, μ is the mean, and σ is the standard deviation.

Now, since the 35th percentile is between 0 and 1, we need to find the corresponding Z-score. Lucky for us, we can use a Z-table (or some fancy math software if you're feeling fancy) to find that Z-score, which should be around -0.3853 (approximately, remember we're using humor, not rocket science here!).

Once we have the Z-score, we can substitute it back into the formula: -0.3853 = (X - 270) / 25. Time to channel our inner algebra skills and solve for X. Cross your fingers and carry the one... Voilà! We find that X ≈ 261.79.

So, the 35th percentile of our normal distribution is around 261.79 (approximately).

To find the 35th percentile of a normal distribution with mean 270 and standard deviation 25, we can use a standard normal distribution table or a calculator with a normal distribution function. Here's how you can do it using a standard normal distribution table:

1. Standardize the value: To use the standard normal distribution table, we need to convert the given percentile to a z-score. The formula for standardizing a value is:
z = (x - μ) / σ
where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the z-score for the 35th percentile. Let's call it z_35. Plugging in the values, we have:
z_35 = (x - 270) / 25

2. Look up the z-score: We can now use the standard normal distribution table to find the corresponding z-score for the desired percentile. The table gives us the area under the curve to the left of a given z-score. We need to find the closest z-score to z_35 in the table and take note of the corresponding area.

For example, if the closest z-score in the table is -0.39 and the corresponding area is 0.6554, it means that 65.54% of the data falls below that z-score, which is equivalent to the 35th percentile.

3. Calculate the value: Now that we know the z-score that corresponds to the 35th percentile, we can reverse the standardization process to find the corresponding value (x) using the formula:
x = μ + z * σ

Substitute the values back into the equation to find the value at the 35th percentile:
x = 270 + z * 25

So, the 35th percentile of the normal distribution with mean 270 and standard deviation 25 can be found by standardizing the value, looking up the z-score in the standard normal distribution table, and then calculating the corresponding value.