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Probability and Logical Conclusion

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

The above situation follows Binomial Distribution (10,0.47)
Therefore Mean = np =10 * 0.47 = 4.7

Variance = npq = 10*0.47*0.53 = 2.491
Standard Deviation = Sqrt(Variance) = 1.578

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.