The number of members in 20 families in a village is given as 6,8,6,3,2,5,7,8,6,5,5,7,7,8,6,6,7,7,6,5

Mathematics

1 answer:

svetoff [14.1K]3 years ago

7 0

Answer:

6,6,6,6,6,6=more than 5

7,7,7,7,7=has exactly 5 members

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A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.53, 0.40

SpyIntel [72]

The mean of the probability distribution is given by the expected value given by

$E(x)=\sum xp(x) \\ \\ =0(0.53)+1(0.40)+2(0.05)+3(0.02) \\ \\ =0.40+0.10+0.06=0.56$

The variance of the probability distribution is given by

$Var(x)=(x-\bar{x})^2p(x) \\ \\ =(0-0.56)^2(0.53)+(1-0.56)^2(0.40)+(2-0.56)^2(0.05)\\+(3-0.56)^2(0.02) \\ \\ =(-0.56)^2(0.53)+0.44^2(0.40)+1.44^2(0.05)+2.44^2(0.02) \\ \\ =0.3136(0.53)+0.1936(0.40)+2.0736(0.05)+5.9536(0.02) \\ \\ =0.166208+0.07744+0.10368+0.119072=0.4664$

The standard deviation is given by

$\sigma(x)=\sqrt{Var(x)} \\ \\ =\sqrt{0.4664}=0.683$