Question

You are looking at the number of multi-million dollar companies in each state. Based on data from last year, you have found a mean of 37 and a standard deviation of 8. Use this information to answer the following question. What is the probability of a randomly selected state having between 21 and 53 multi-million dollars

Answer 1

By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars

Explanation:

We have no information about the distribution, so we use the Chebyshev's theorem to solve this question.

Chebyshev Theorem:

75% of the data within 2 standard deviations of the mean.

89% of the data within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 37

Standard deviation = 8

What is the probability of a randomly selected state having between 21 and 53 multi-million dollars

21 = 37 - 2*8

So 21 is 2 standard deviations below the mean.

53 = 37 + 2*8

So 52 is 2 standard deviations above the mean.

By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars