the average purchase per customer is 42 with a standard deviation of 4.36. using Chebysevs theorem what percentage of people will make a purchase between 54 and 30
I got 94.7 percent but i am unsure if its the correct answer can anyone verify this for me thanks
At least 86.7988889 is what I got.
(1-1/(12/4.36)^2
http://www.gseis.ucla.edu/courses/ed230a2/chebyshev.html
Thanks i see where i went wrong
To verify the answer using Chebyshev's theorem, you can follow these steps:
1. Calculate the z-scores for each value.
- For 54: (54 - 42) / 4.36 = 2.75
- For 30: (30 - 42) / 4.36 = -2.75
2. Chebyshev's theorem states that for any constant k, the percentage of data within k standard deviations of the mean is at least (1 - 1/k^2). In this case, k = 2.75.
3. Substitute the value of k into the formula to find the minimum percentage of data within the range of 30 to 54:
- (1 - 1/2.75^2) = 1 - 1/7.5625 ≈ 0.868
4. Multiply the result by 100 to convert it to a percentage:
- 0.868 * 100 ≈ 86.8%
Therefore, according to Chebyshev's theorem, at least 86.8% of people will make a purchase between 54 and 30. Since your answer of 94.7% is higher, it is possible that you used a different method or made a calculation error.