Suppose that for a given computer salesperson, the table below gave the probability distribution of x = the number of systems sold in 1 month.X12345678P(x)0.010.120.100.300.300.110.010.05 Calculate the mean value of x (the mean number of systems sold).Calculate the variance and standard deviation of x. How would you interpret these values?What is the probability that the number of systems sold is within 1 standard deviation of its mean value?What is the probability that the number of systems sold is more than 2 standard deviations from the mean?

For ease of calculations, we construct the following table: X P(X) X. P(X) (x-X_bar)…

Answered: Suppose that for a given computer…

A First Course in Probability (10th Edition)

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Suppose that for a given computer salesperson, the table below gave the probability distribution of x = the number of systems sold in 1 month.

X	1	2	3	4	5	6	7	8
P(x)	0.01	0.12	0.10	0.30	0.30	0.11	0.01	0.05

Calculate the mean value of x (the mean number of systems sold).
Calculate the variance and standard deviation of x. How would you interpret these values?
What is the probability that the number of systems sold is within 1 standard deviation of its mean value?
What is the probability that the number of systems sold is more than 2 standard deviations from the mean?

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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