##### Televisions: The number of televisions per household in a small town.

label Statistics
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Televisions: The number of televisions per household in a small town.

Televisions   0     1     2     3
Households    26   442   728   1404

(a) Use the frequency distribution to construct a probability distribution.
(b) Graph the probability distribution using a histogram and describe its shape.
(c) Find the mean, variance, and standard deviation of the probability distribution.
(d) Interpret the results in the context of the real life situation.

Mar 26th, 2015

(a) Let x represent the number of televisions for a randomly selected household. Construct a probability distribution for the above data:

x 0 1 2 3

P(x)  For x = 0, 1, 2 , 3 are.

P(0) = 26/ 2600 = 0.01

P(1) = 442/2600 = 0.17

P(2) = 728/ 2600 = 0.28

P(3) = 1404/ 2600 = 0.54

(b) Calculate the mean of the probability distribution.

µ = XxP(x) = 0 · 0.01 + 1 · 0.17 + 2 · 0.28 + 3 · 0.54 = 2.35

(c) Calculate the standard deviation of the probability distribution. σ 2 = X(x − µ) 2P(x) = (0 − 2.35)2 · 0.01 + (1 − 2.35)2 · 0.17 + (2 − 2.35)2 · 0.28 + (3 − 2.35)2 · 0.54 = 0.6275 σ = √ 0.6275 = 0.792

Mar 26th, 2015

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Mar 26th, 2015
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Mar 26th, 2015
Oct 17th, 2017
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