A set of data is normally distributed with a mean of 455 and a standard deviation of 25. What percent of the data is in the interval 405–455?
To find the percentage of data within a specific interval, we can use the concept of z-scores.
First, let's calculate the z-scores for the lower and upper limits of the interval. The z-score represents the number of standard deviations an observation is away from the mean.
For the lower limit, 405:
z = (x - μ) / σ
z = (405 - 455) / 25
z = -2
For the upper limit, 455:
z = (x - μ) / σ
z = (455 - 455) / 25
z = 0
Next, we need to find the area under the normal curve between these z-scores.
Using a standard normal distribution table or a calculator, we can find the area associated with each z-score.
For z = -2, the area is approximately 0.0228.
For z = 0, the area is approximately 0.5.
To find the percentage, we subtract the area for the lower z-score from the area for the upper z-score and multiply by 100.
percentage = (0.5 - 0.0228) * 100
percentage = 0.4772 * 100
percentage = 47.72%
Therefore, approximately 47.72% of the data is within the interval 405-455.
One is the mean.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the Z score. Multiply by 100.