The 68-95 Rule for Probability: I

Belinda plans to take a simple random sample of size 64 from a population, and to take the mean x-bar of heights of the people in the sample. Unknown to Belinda, the SD of the population happens to be 16 inches, so the SD of x-bar is

16/sqrt(64)

## [1] 2

Match each chance with its approximate value from the choices in the attached picture

Group of answer choices

(1) The chance that x-bar will be 2 or more inches below the mean of the population.

(2)The chance that x-bar will be within 4 inches of the mean of the population.

( 3) The chance that x-bar will be more than 6 inches above the mean of the population.

(4) The chance that x-bar will be within 6 inches of the mean of the population.

(5) The chance that x-bar will be within 4 inches of the mean of the sample.

v [ Choose ]
0.15%
16%
100%. (After all, x-bar IS the mean of the sample!)
95%
99.7%

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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