A set of data has a normal distribution with a mean of 29 and a
standard deviation of 4. Find the percent of data within the
interval 25 to 33.
To find the percent of data within the interval 25 to 33, we need to find the area under the normal curve between these two values.
First, we need to standardize the values using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For 25:
z = (25 - 29) / 4 = -1
For 33:
z = (33 - 29) / 4 = 1
Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-values.
Using a calculator, we can find that the area between -1 and 1 is approximately 0.6827.
To convert this to a percentage, we multiply by 100:
0.6827 x 100 = 68.27%
Therefore, approximately 68.27% of the data falls within the interval 25 to 33.