Question

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

Answer 1

Answer: The mininum percentage of recent graduates is 88.9%

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:

`\%=1-(1)/(k^2)` .....(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:

`\Rightarrow (3300)/(1100)=3=k`

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

`\%=1-(1)/(3^2)\\\\\%1-(1)/(9)\\\\\%=(8)/(9)=88.9\%{`

Hence, the mininum percentage of recent graduates is 88.9%