Please provide formulas and logical conclusions for each. Include step by step calculations for each.
8. If the probability of having a boy is .47, find the following
a. For families with 10 children
i. The mean for the number of boys in a family
ii. The standard deviation for the number of boys
iii. The probability of having exactly 4 boys
iv. The probability of having at least 4 girls
b. What is the probability that the first girl would be the third born?
c. Use the normal approximation to find the probability that in 200 births, less than 140 are boys.
Solution Preview
a.
i.
The above situation follows Binomial Distribution (10,0.47)
Therefore Mean = np =10 * 0.47 = 4.7
ii.
Variance = npq = 10*0.47*0.53 = 2.491
Standard Deviation = Sqrt(Variance) = 1.578
iii.
P(X = 4) = 10C4 * 0.474 * 0.536
= 0.227125
iv. P(X≥ 4 girls) = 1 ...
Solution Summary
In the following posting, probability and logical conclusions are analyzed for various scenarios. Step by step calculations are provided for each problem.
... be a relationship between reason and conclusion in inductive ... example if we have a deductive logic example ... 1. How would you apply probability concepts, such as ...
... the truth of its conclusion, "Helen went to ... Two methods of logical reasoning are deductive ... b) Inductive: Diverse facts, probability, generalizations, hypotheses ...
... truth: o The truth of logical correctness has ... presented, truly support (ie, structurally support) the conclusion. ... sort of sliding scale of probability, but the ...
... Anthony may have a greater probability of experiencing ... premises are true Test 2: Logical Strength Even ... both premises are true the conclusion is faulty. ...
... such as categorical logic, propositional logic, and predicate logic. ... we must not mistake the probabilities involved ... but will simply attack the conclusion of the ...
... of reasoning Does not always mean conclusion is false ...Logic. ... Diverse facts, probability, generalizations, hypotheses, analogies inductive strength. ...
... of reasoning Does not always mean conclusion is false ...Logic. ... Diverse facts, probability, generalizations, hypotheses, analogies inductive strength. ...
... merely reduce it, even if the probability of a ... Some decisions assert personal preferences over logical choice. ... as luck by 'reading' into probabilities and most ...
... show that it has a high probability of happening ... explicitly the assumptions needed to derive the conclusion. ... sometimes be a hindrance to logical decision making ...
