Ram earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100.what proportion of student had a higher score than Ram?(Assume that test scores are normally distributed)
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.
To solve this problem, we need to use the z-score formula and the standardization process.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
z = z-score
x = individual test score
μ = mean test score
σ = standard deviation
In this case,
x = 940
μ = 850
σ = 100
Substituting these values into the formula, we can find the z-score:
z = (940 - 850) / 100
z = 90 / 100
z = 0.9
Now, we need to find the proportion of students who scored higher than Ram. We can look up this proportion in the standard normal distribution table using the z-score obtained.
The standard normal distribution table gives us the proportion of values below a certain z-score. To find the proportion of values above a certain z-score, we subtract the corresponding proportion from 1.
Looking up the z-score of 0.9 in the standard normal distribution table, we find the corresponding proportion is 0.8159.
However, we need the proportion of students who scored higher than Ram, so we subtract this value from 1:
Proportion = 1 - 0.8159
Proportion = 0.1841
Therefore, approximately 18.41% of students had a higher score than Ram on the test.
To find the proportion of students who had a higher score than Ram, we need to calculate the Z-score for Ram's score and then find the area under the normal curve corresponding to scores higher than Ram's.
First, we calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = Ram's score = 940
μ = Mean test score = 850
σ = Standard deviation = 100
Z = (940 - 850) / 100 = 0.9
Next, we need to find the proportion of scores higher than Ram's by finding the area under the normal curve to the right of the Z-score of 0.9. This can be done using a standard normal distribution table or by using a calculator or statistical software.
Using a calculator or software:
We can use a calculator or software with a standard normal distribution function to find the area to the right of Z = 0.9. The area will give us the proportion of scores higher than Ram's.
Using a standard normal distribution table:
If using a standard normal distribution table, we would need to find the area corresponding to Z = 0.9. We need to find the value in the table that is closest to 0.9 and then look for the corresponding area in the table.
Once we have the area under the normal curve, we subtract it from 1 to find the proportion of scores higher than Ram's.
The final proportion of students who had a higher score than Ram can be interpreted as the percentage by multiplying it by 100.