The SAT this year has a mean of 500 and a standard deviation of 50. What percent of students scored between 400 and 600?
Your question is perfectly suitable for this application, just enter the data
http://davidmlane.com/normal.html
To find the percentage of students who scored between 400 and 600 on the SAT, we can use the concept of standard deviation.
First, let's convert the given scores into z-scores by using the formula:
z = (x - μ) / σ
where z is the z-score, x is the individual score, μ is the mean, and σ is the standard deviation.
For the lower score of 400:
z = (400 - 500) / 50
= -100 / 50
= -2
For the higher score of 600:
z = (600 - 500) / 50
= 100 / 50
= 2
Now that we have the z-scores, we can use a standard normal distribution table or a statistical calculator to find the percentage of students who scored between these z-scores.
A standard normal distribution table provides the percentage of values that fall below a certain value in a standard normal distribution. Since we have a standard normal distribution table, we can find the percentage for z = -2 and z = 2.
Looking up the z-scores -2 and 2 in the standard normal distribution table, we find the following percentages:
For z = -2: 2.28%
For z = 2: 97.72%
To find the percentage of students who scored between 400 and 600, we need to find the area under the curve between the z-scores -2 and 2. Subtracting the area below z = -2 from the area below z = 2 gives us:
97.72% - 2.28% = 95.44%
Therefore, approximately 95.44% of students scored between 400 and 600 on the SAT this year.