set of data is normally distributed with a mean of 200 and standard deviation of 50.

· What would be the standard score for a score of 300?
· What percentage of scores is between 200 and 300?
· What would be the percentile rank for a score of 300?
(Points : 6)

1) 300 is two deviations of 50 away from 200, so the standard score is 2.

2) You need to look at a normal distribution for this. A quick google search should help you just fine. Or, possibly, you were provided one in class.

From such a table, you can see that being two deviations away from the middle amounts to 34.13% + 13.59% = 47.72%

3) You just take 47.72% 9which is the distance from the middle to 300) and add 50% (which is everyone below the middle). You get 97.72%

1. Z (a standard score) = (score-mean/SD)

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

Percentile rank is the proportion below or equal to a particular score.

Oh, let's dive into some statistical humor!

What would be the standard score for a score of 300? Well, the formula for the standard score (z-score) is (X - mean) / standard deviation. Plugging in the values, we get (300 - 200) / 50 = 2. That means a score of 300 is 2 standard deviations above the mean. That's pretty high up there, like a clown on stilts!

What percentage of scores is between 200 and 300? To find that out, we need to calculate the z-scores for both scores. The z-score for 200 is (200 - 200) / 50 = 0, and the z-score for 300 is (300 - 200) / 50 = 2. Using z-tables, we can find that the percentage of scores between 0 and 2 z-score is about 47.72%. So, approximately 47.72% of scores are between 200 and 300. Not quite half, but close enough to make it interesting!

What would be the percentile rank for a score of 300? A percentile rank represents the percentage of scores that are equal to or below a given score. To find it, we use the z-score and convert it to a percentile using the z-tables. For a z-score of 2, the percentile is about 97.72%. So, a score of 300 would have a percentile rank of approximately 97.72%. Almost at the top of the clown ladder!

Hope this statistical circus act brought a smile to your face!

To answer each question step-by-step:

1. Calculate the standard score (also known as z-score) for a score of 300:
The standard score (Z-score) is a measure of how many standard deviations an individual score is from the mean of a distribution.
Standard score (Z-score) = (x - mean) / standard deviation
In this case, the score is 300, mean is 200, and standard deviation is 50.
Standard score (Z-score) = (300 - 200) / 50 = 2

2. Calculate the percentage of scores between 200 and 300:
To find the percentage of scores between two values in a normal distribution, we need to convert the values into z-scores and then find the corresponding area under the normal curve.
Using a standard normal distribution table (Z-table) or a statistical software, we can find the area between two z-scores.
For our case, the z-score for 200 is:
Z1 = (200 - 200) / 50 = 0
And the z-score for 300 is:
Z2 = (300 - 200) / 50 = 2
The percentage of scores between 200 and 300 is the difference between the cumulative areas corresponding to Z1 and Z2.
Using a Z-table, we can find that the area corresponding to Z1 is 0.5000 and the area corresponding to Z2 is 0.9772.
So, the percentage of scores between 200 and 300 is 0.9772 - 0.5000 = 0.4772 or 47.72%.

3. Calculate the percentile rank for a score of 300:
Percentile rank is the percentage of scores that fall at or below a given score.
We can use the cumulative area under the normal curve to find the percentile rank of a specific score.
For our case, the z-score for 300 is 2 (calculated in step 1).
Using a Z-table, we can find the area corresponding to a Z-score of 2, which is 0.9772.
The percentile rank for a score of 300 is 0.9772 or 97.72%.

To answer these questions, you will need to use the concept of z-scores and the standard normal distribution table.

1. What would be the standard score for a score of 300?
The standard score, also known as the z-score, measures how many standard deviations a particular score is away from the mean of the distribution. To calculate the z-score, you can use the formula: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation.

In this case, the score is 300, the mean is 200, and the standard deviation is 50. Substituting these values into the formula, we get z = (300 - 200) / 50 = 2. The standard score for a score of 300 is 2.

2. What percentage of scores is between 200 and 300?
To find the percentage of scores between two values in a normally distributed data set, you can use the standard normal distribution table. This table provides the area under the curve corresponding to different z-scores.

First, find the z-score for the lower boundary (200) and the z-score for the upper boundary (300) using the formula from the previous step. In this case, the z-score for 200 is (200 - 200) / 50 = 0, and the z-score for 300 is (300 - 200) / 50 = 2.

Next, look up the area under the curve for each z-score in the standard normal distribution table. The table will give you the area to the left of the z-score. For a z-score of 0, the area is 0.5000, and for a z-score of 2, the area is 0.9772.

To find the percentage of scores between 200 and 300, subtract the smaller area from the larger area: 0.9772 - 0.5000 = 0.4772. So, approximately 47.72% of scores are between 200 and 300.

3. What would be the percentile rank for a score of 300?
The percentile rank represents the percentage of scores that are equal to or below a particular score. To find the percentile rank, you can use the z-score and the standard normal distribution table.

First, find the z-score for the score of 300 using the formula from the first question. In this case, the z-score is 2.

Next, look up the area under the curve for the z-score of 2 in the standard normal distribution table. The table will give you the area to the left of the z-score. The area for a z-score of 2 is 0.9772.

To find the percentile rank, multiply the area by 100: 0.9772 * 100 = 97.72%. So, the percentile rank for a score of 300 is approximately 97.72%.