The mean score on a driving exam for a group of​ driver's education students is 84 ​points, with a standard deviation of 6 points. Apply​ Chebychev's Theorem to the data using k=2. Interpret the results. At least _% of the exam scores fall between _ and _.
Simplify your answers.

At least 75% of the exam scores fall between 72 and 96.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by .

Apply​ Chebychev's Theorem to the data using k=2.

k = 2, so within 2 standard deviations of the mean, interval in which at least 75% of the measures fall.

In this question:

Mean of 84, standard deviation of 6.

84 - 2*6 = 84 - 12 = 72

84 + 2*6 = 84 + 12 = 96

At least 75% of the exam scores fall between 72 and 96.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.