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

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

Step-by-step 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

14 ft 7 inches

step-by-step explanation:

since each model inch corresponds to 25 real inches, 7 model inches will correspond to

7×25" = 175"

at 12" per foot, that is 14 feet, 7 inches.