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Suppose that salaries for recent graduates of one university have a mean of $24,800 with a standard deviation of $1100. Using Chebyshev's Theorem, what is the minimum percentage of recent graduates who have salaries between $21,500 and $28,100

Respuesta :

Answer: The mininum percentage of recent graduates is 88.9%

Step-by-step explanation:

We are given:

Mean value = $24,800

Standard deviation = $1100

Minimum value of salary = %21,500

Maximum value of salary = %28,100

The equation for Chebyshev's Theorem is given by:

[tex]\%=1-\frac{1}{k^2}[/tex]           .....(1)

To calculate the value of 'k', we first subtract the mean value from the maximum value.

⇒ [28,100 - 24,800] = 3300

Secondly, dividing the above-calculated value by the standard deviation, we get:

[tex]\Rightarrow \frac{3300}{1100}=3=k[/tex]

Putting value of 'k' in equation 1, we get:

[tex]\%=1-\frac{1}{3^2}\\\\\%1-\frac{1}{9}\\\\\%=\frac{8}{9}=88.9\%{[/tex]

Hence, the mininum percentage of recent graduates is 88.9%

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