Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. A score of 560 reprecents what percentile? Please round answer to the neareast tenth.
I'm basicly confused on the formula and how the numbers are in the fromlua
Use Z score equation and find table in the back of your statistics text labeled something like "areas under normal distribution" to find the precentile related to the Z score.
To find the percentile of a given score in a normal distribution, you can use the Z-score formula. The Z-score measures the number of standard deviations a given value is from the mean. The formula to calculate the Z-score is:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value you want to find the percentile for (in this case, 560)
μ is the mean of the distribution (500)
σ is the standard deviation (100)
Calculating the Z-score for a score of 560:
Z = (560 - 500) / 100
Z = 60 / 100
Z = 0.6
Now that we have the Z-score, we can look up the corresponding percentile using a Z-table or a statistical calculator. The percentile is the percentage of scores that fall below a given value.
Using a Z-table or calculator, we find that a Z-score of 0.6 corresponds to a percentile of approximately 72.2%. Rounded to the nearest tenth, the 560 SAT score represents the 72.2 percentile.