# Chebyshev's Theorem: need help urgent

• Sep 15th 2008, 07:17 PM
Mike Bell
Chebyshev's Theorem: need help urgent
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.
• Sep 16th 2008, 01:25 AM
mr fantastic
Quote:

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

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

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