A set of data is normally distributed with a mean of 16 and a standard deviation of 0.03. What percent of the data is between 15.2 and 16?
16-15.2 = 0.8
0.8/0.03 = n = 26 standard deviations
so,
erf(n/sqrt(2)) = approximately 1
so,
50% of the data would be between 15.2 and 16.
Are you sure there are no typos in your data?
If so, find the Z scores for both scores.
Z = (score-mean)/Standard deviation
In the back of your stat text, find the Z scores in a table labeled something like "areas under the normal distribution." Find the proportion between the two scores and convert to a percentage.
To find the percentage of data that falls between two values in a normal distribution, you need to calculate the area under the normal curve between those two values.
First, let's standardize the values of 15.2 and 16 using the formula:
z = (x - mean) / standard deviation
For 15.2:
z = (15.2 - 16) / 0.03
For 16:
z = (16 - 16) / 0.03
Calculating these values will give us the standardized z-scores for both values.
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.
Alternatively, we can use statistical software to calculate the area. Using the z-scores calculated above, we can find the area (probability) between 15.2 and 16. The result will be the percentage of the data that falls within this range.