Question

true or false: standard deviation tells you the distance from the lowest value up to the highest value.

• 3 points

true
false
true or false: chebychevs theorem does not work within 1 standard deviation of the mean.

• 3 points

true
false
chebychevs theorem:
the mean time in a womens 200 - meter dash is 43 seconds, with a standard deviation of 0.2 seconds. if k = 2, 75% of the data falls between which two values?
choose

Explanation:

First Question:

Step1: Recall the definition of standard deviation

Standard deviation measures the dispersion of data around the mean, not the distance from the lowest to the highest value (which is the range).

Second Question:

Step1: Recall Chebyshev's Theorem formula

Chebyshev's Theorem states that for any number \(k> 0\), at least \(1-\frac{1}{k^{2}}\) of the data lies within \(k\) standard deviations of the mean. When \(k = 1\), \(1-\frac{1}{k^{2}}=1 - 1=0\). Since we can't have a negative proportion of data, and the formula gives a non - meaningful result for \(k = 1\), Chebyshev's Theorem does not work within \(1\) standard deviation of the mean.

Third Question:

Step1: Use Chebyshev's formula for bounds

The formula for the bounds is \(\mu\pm k\sigma\). Given \(\mu = 43\) (mean), \(\sigma=0.2\) (standard deviation), and \(k = 2\).

Step2: Calculate the lower bound

The lower bound is \(\mu - k\sigma=43-2\times0.2=43 - 0.4 = 42.6\).

Step3: Calculate the upper bound

The upper bound is \(\mu + k\sigma=43 + 2\times0.2=43+0.4 = 43.4\).

Answer:

1. B. False
2. A. True
3. The two values are \(42.6\) and \(43.4\)