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

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Mathematics

Description

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.

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Explanation & Answer

(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


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