Question

test 1
score: 8.72/10 answered: 9/10
question 10
historically, heights of men have a mean of 169.5 cm and a standard deviation of 8.8 cm.
use chebyshev’s rule to approximate the percentage of men between 134.3 cm and 204.7 cm.
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Explanation:

Step1: Calculate the number of standard deviations ($k$)

The formula for the number of standard deviations from the mean is $k=\frac{x - \mu}{\sigma}$.
For the lower bound: $x_1 = 134.3$, $\mu=169.5$, $\sigma = 8.8$. Then $k_1=\frac{169.5 - 134.3}{8.8}=\frac{35.2}{8.8} = 4$.
For the upper bound: $x_2 = 204.7$, $\mu = 169.5$, $\sigma=8.8$. Then $k_2=\frac{204.7 - 169.5}{8.8}=\frac{35.2}{8.8}=4$.

Step2: Apply Chebyshev's Rule

Chebyshev's Rule states that the proportion of data within $k$ standard deviations of the mean is at least $1-\frac{1}{k^{2}}$.
Substitute $k = 4$ into the formula: $1-\frac{1}{4^{2}}=1-\frac{1}{16}=\frac{16 - 1}{16}=\frac{15}{16}=0.9375 = 93.75\%$

Answer:

at least 93.75%