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Math Help - Chebyshev's Theorem: need help urgent

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    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.
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    Quote Originally Posted by Mike Bell View Post
    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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