Multiple Choice
Which of the following is true about ?
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3. Describing Data Numerically
Standard Deviation
Multiple Choice
Suppose the weights of a group of students are normally distributed with a mean of and a standard deviation of . Which of the following weights are within standard deviations of the mean? Select three options.
A
kg
B
kg
C
kg
D
kg
Verified step by step guidance1
Identify the mean (\(\mu\)) and standard deviation (\(\sigma\)) of the normal distribution. Here, \(\mu\) = 70 \(\text{ kg}\) and \(\sigma\) = 5 \(\text{ kg}\).
Calculate the range that lies within 2 standard deviations from the mean. This range is given by: \(\mu - 2\sigma\) to \(\mu + 2\sigma\).
Substitute the values into the formula: lower bound = \(70 - 2 \times 5\), upper bound = \(70 + 2 \times 5\).
Simplify the bounds to find the interval of weights within 2 standard deviations of the mean.
Check each given weight to see if it falls within this interval. Those weights that lie between the lower and upper bounds are within 2 standard deviations of the mean.
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