The graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic.
Which weights are within 2 standard deviations of the mean? Check all that apply.
well, if you know the mean and the std,
µ-2σ <= x <= µ+2σ
To determine which weights are within 2 standard deviations of the mean, we need to understand the concept of the standard deviation in a normal distribution.
Standard deviation measures the spread or dispersion of data around the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and roughly 99.7% within three standard deviations.
To find the weights within 2 standard deviations of the mean, we need to calculate the lower and upper bounds.
1. Find the Mean (the average weight recorded).
2. Find the Standard Deviation (the measure of dispersion).
3. Calculate the Lower Bound: Mean - (2 x Standard Deviation).
4. Calculate the Upper Bound: Mean + (2 x Standard Deviation).
By performing these calculations, we can identify the weight range within 2 standard deviations of the mean.
To determine which weights are within 2 standard deviations of the mean, we need to identify the area under the normal distribution curve.
For a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. This means that weights within this range are considered to be the most common or average.
So, to answer the question, the weights within 2 standard deviations of the mean are checked.