Please help with the following statistics question, Suppose the number of recall

Question

Please help with the following statistics question,

Suppose the number of recalls of children's clothing during a given month is a random variable with probability distribution given in the table below. Verify that this is a valid probability distribution. Calculate the mean number of recalls of children's clothing during a given month. Use the correct notation. Calculate die standard deviation for this probability distribution. Use the correct notation. If the number of recalls in a given month is more than one standard deviation above the mean, the federal government issues a special warning directed toward parents. What is the probability that a special warning will be issued during a given month?

Explanation / Answer

a)

The probabilities should add up to 1.

Thus,

0.005 + 0.185 + 0.275 + 0.305 + 0.200 + 0.020 + 0.010

= 1 [Thus, it is a valid probability distribution]

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b)

Consider the table:

Thus,  
  
E(x) =    2.61 [ANSWER]

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C)

Var(x) = E(x^2) - E(x)^2 =    1.2779
Therefore,

s(x) =    1.130442391 [ANSWER]

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D)

E(x) + s(x) = 3.740442391

Thus, if it exceeds 3.7, it will be given a warning, which is, when x is at least 4.

P(at least 4) = P(4) + P(5) + P(6) = 0.2 + 0.02 + 0.01 = 0.23 [answer]

x P(x) x P(x) x^2 P(x) 0 0.005 0 0 1 0.185 0.185 0.185 2 0.275 0.55 1.1 3 0.305 0.915 2.745 4 0.2 0.8 3.2 5 0.02 0.1 0.5 6 0.01 0.06 0.36

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