Chebyshev's Theorem: need help urgent

**Mike Bell** · September 15th 2008, 07:17 PM

The times scuba divers can stay underwater at a depth of 40 feet has a mean of 50 minutes with a standard deviation of 4 minutes.

Use chebyshevs theorem to decide what times at least 75% of all divers can stay under water.

do the same for 89% of the divers.

**mr fantastic** · September 16th 2008, 01:25 AM

Originally Posted by Mike Bell

The times scuba divers can stay underwater at a depth of 40 feet has a mean of 50 minutes with a standard deviation of 4 minutes.

Use chebyshevs theorem to decide what times at least 75% of all divers can stay under water.

do the same for 89% of the divers.

Chebyshev's Theorem: $\Pr( |X - \mu| < k \sigma) \geq 1 - \frac{1}{k^2}$ .

That is, $\Pr(\mu - k \sigma < X < \mu + k \sigma) \geq 1 - \frac{1}{k^2}$ .

Now note that $1 - \frac{1}{k^2} = 0.75 \Rightarrow k = 2$ and $1 - \frac{1}{k^2} = 0.89 \Rightarrow k \approx 3$ .

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