a set of data is normally distributed with a mean of 1000 and a standard deviation of 100.what would be standard score for a score of 900.what percent of scores is betyween 1000 and 900.what would be percentile rank for a score of 900.
Z is one type of standard score.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score. Multiply by 100 to change proportion to percent.
To find the standard score (also known as z-score) for a given score, you can use the formula:
z = (x - μ) / σ
Where:
- z is the standard score,
- x is the given score,
- μ is the mean of the distribution,
- σ is the standard deviation of the distribution.
Using this formula, let's find the standard score for a score of 900:
z = (900 - 1000) / 100
z = -1
So, the standard score for a score of 900 is -1.
To find the percentage of scores between 1000 and 900 in a normal distribution, we need to calculate the area under the curve between those two scores.
First, we find the z-scores for the two scores using the formula mentioned earlier:
z1 = (1000 - 1000) / 100 = 0
z2 = (900 - 1000) / 100 = -1
Next, we use a standard normal distribution table (also known as the z-table) or a calculator to find the area (probability) corresponding to each z-score.
From the z-table, the area to the left of z = 0 is 0.5000, and the area to the left of z = -1 is 0.1587.
To find the percentage between these two z-scores:
Percentage = (area to the left of z2) - (area to the left of z1)
= 0.1587 - 0.5000
= 0.3413
So, approximately 34.13% of scores lie between 1000 and 900 in a normally distributed set of data.
The percentile rank of a score represents the percentage of scores that are equal to or below that score. To calculate the percentile rank for a score of 900, we need to find the area to the left of that score.
Using the z-score formula:
z = (900 - 1000) / 100
z = -1
From the z-table, we find that the area to the left of z = -1 is 0.1587, which is approximately 15.87%.
So, the percentile rank for a score of 900 is approximately 15.87%.