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Suppose that salaries for recent graduates of one university have a mean of $26,400$ 26,400 with a standard deviation of $1200$ 1200. Using Chebyshev's Theorem, what is the minimum percentage of recent graduates who have salaries between $22,800$ 22,800 and $30,000$ 30,000? Round your answer to one decimal place.

Respuesta :

Answer:

By the Chebyshev's Theorem, the minimum percentage of recent graduates who have salaries $22,800 and $30,000 is 89%.

Step-by-step explanation:

Chebyshev's theorem states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 26,400

Standard deviation = 1200

Between $22,800 and $30,000

22800 = 26400 - 3*1200

So 22800 is 3 standard deviations below the mean

30000 = 26400 + 3*1200

So 30000 is 3 standard deviations above the mean.

By the Chebyshev's Theorem, the minimum percentage of recent graduates who have salaries $22,800 and $30,000 is 89%.

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