Refer to the tabic below which describes results from groups of 10 births from 1

Question

Refer to the tabic below which describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Find the mean and standard deviation for the numbers of girls in 10 births Find the probability of getting exactly 1 girl in 10 births. Find the probability of getting 1 or fewer girls in 10 births. Which probability is relevant for determining whether 1 is an unusually low number of girls in 10 births: the result from part (a) or part (b)? Is 1 an unusually low number of girls in 10 births? Why or why not?

Explanation / Answer

a)

Consider:

Hence,

Thus,  
  
E(x) = Expected value = mean =    5 [ANSWER]

Var(x) = E(x^2) - E(x)^2 =    2.508

s(x) = sqrt [Var(x)] =    1.583666632 [ANSWER, STANDARD DEVIATION]

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2.

P(1) = 0.01 [ANSWER, GIVEN]

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c.

P(at most 1) = P(0) + P(1) = 0.001 + 0.010 = 0.011 [ANSWER]

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d)

The one in part c [1 or fewer girls].

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e)

Yes, because it has a probability of 0.011 < 0.05, as in part c.

x P(x) x P(x) x^2 P(x) 0 0.001 0 0 1 0.01 0.01 0.01 2 0.044 0.088 0.176 3 0.117 0.351 1.053 4 0.205 0.82 3.28 5 0.246 1.23 6.15 6 0.205 1.23 7.38 7 0.117 0.819 5.733 8 0.044 0.352 2.816 9 0.01 0.09 0.81 10 0.001 0.01 0.1

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