Answer:
Interpreting the results:
a) At least 99.3% of the data lies between 12 standard deviations of the mean
b) The data lies between points 0 and 168
Explanation:
The mean score on a driving exam for a group of driver's education students is 84 points, with a standard deviation of 5 points. Apply chebychev's theorem to the data using k= 12 interpret the results
Chebychev's theorem states that:
At least 1 - 1/k² data lies between k standard deviation of the mean
μ ± kσ
Where k is a positive number greater than 1
From the question above
μ = Mean = 84 points
σ = Standard deviation = 5 points
Hence: k = 12
We have:
1 - 1/12²
= 1 - 1/144
= 144 - 1/144
= 143/144
= 0.9930555556
Approximately = 99.3%
Interpreting these results means that At least 99.3% of the data lies between 12 standard deviations of the mean
Hence,
μ - kσ
84 - 12 × 7
= 84 - 84
= 0
μ + kσ
84 + 12 × 7
= 84 + 84
= 168
Hence, the data lies between points 0 and 168