# Math Help - Chebyshev's Theorem: need help urgent

1. ## 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.

2. 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 $1 - \frac{1}{k^2} = 0.89 \Rightarrow k \approx 3$.