The mean sale per customer for 40 customers at a gas station i...

Question

The mean sale per customer for 40 customers at a gas station is $32.00, with a standard deviation of $4.00. Using Chebychev’s Theorem, determine at least how many of the customers spent between $24.00 and $40.00.

Accepted Answer

All right, hello everyone. This question says, at a coffee shop, the mean expenditure per customer for 60 customers is $10 with a standard deviation of $2. According to Chebyshev's theorem, what is the minimum number of customers who spent between $6.14 dollars? Option A says 22, B says 38, C says 45, and D says 54. So, What information do we currently have for starters? Well, first we know that mew. Which is the mean for the population is equal to 10. And sigma, that's the standard deviation, is equal to 2. Now, the lower bound in this case is $6 and the upper bound is $14. Recall that Chebyshev's theorem states that for any distribution, at least one subtracted by one over. K squared Of the data values must fall within K standard deviations of the mean where K is greater than 1. So, Recall that the lower and upper bounds can be expressed as mew. Added to or subtracted by. K multiplied by sigma. So using This expression we can solve for K. So here, for example, 10. Subtracted by K multiplied by sigma equals 6, that's the lower bound of the interval. Plugging in the information we already have, that's 10, subtracted by K multiplied by 2 equals 6. So is equal to 10, subtracted by 6 divided by 2. Which equals 2. So now Now that we have what K happens to be, we can apply Chevyshev's theorem. So the minimum proportion. As mentioned before, was one subtracted by 1 over k squared. So, the minimum proportion or MP is 1 subtracted by 1 divided by 2 squared. Which is 1 subtracted by 1/4, which gives you 3/4. And now, you can find the minimum number of customers by multiplying the minimum proportion by the total number of customers. So 3 quarters Multiplied by 60. Equals 45. Which means that according to Chevy Cheev's theorem, at least 45 customers spent between $6.14 dollars. Meaning C is our correct answer. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

The mean sale per customer for 40 customers at a gas station is $32.00, with a standard deviation of $4.00. Using Chebychev’s Theorem, determine at least how many of the customers spent between $24.00 and $40.00.

Key Concepts

Mean

Standard Deviation

Chebyshev's Theorem

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