College

University graduates have a mean job search time of 38.1 weeks, with a standard deviation of 10.1 weeks. The distribution of job search times is not assumed to be symmetric. Between what two search times does Chebyshev's Theorem guarantee that we will find at least 89% of the graduates?

Answer :

Final answer:

Using Chebyshev's Theorem, we can conclude that at least 89% of university graduates will find a job between approximately 23.14 and 53.06 weeks.

Explanation:

In Mathematics, specifically statistics, Chebyshev's Theorem provides us with a way to know the minimum proportion of data within k standard deviations of the mean for any distribution. To find at least 89% of the graduates, we calculate k using the formula 1/(1-k²). Rearranging the formula yields k² = 1 - 1/0.89. Solving for k gives k ≈1.48. Given a mean of 38.1 weeks and a standard deviation of 10.1 weeks, we multiply k by the standard deviation and add/subtract the result from the mean. This gives us the range, from approximately 23.14 to 53.06 weeks, within which Chebyshev's Theorem guarantees that at least 89% of university graduates will find a job.

Learn more about Chebyshev's Theorem here:

https://brainly.com/question/34274356

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