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# binominal distribution and probability

Please show all work and some explanation as to why you chose the formula you did.

Part 1.
In some countries, girls are valued much less than boys. Sometimes women in such countries abort fetuses known to be girls and many girl babies are victims of infanticide. Suppose there are 43 girls to every 57 boys who reach age 1 in one such country.

(10). What is the probability that a family with three children (all over 1 year of age) has 2 boys and 1 girl?

(11). What is the probability that this family will have at least 2 boys?

Choose the correct answers for questions 10-11 from the following list.
(A)0.324 (B)0.140 (C)0.464 (D)0.185 (E)0.509 (F)0.604 (G)0.419 (H)0.772 (I)0.164 (J)0.273

Part 2.
Mortality tables enable actuaries to obtain the probability that a person, at some age, will live a specified number of years. One particular set of mortality tables indicates that a person who has lived to be 20 years of age has a probability of 0.80 of subsequently living at least until the age of 65.

In questions (37) and (38), suppose six (6) friends taking a course in Statistics are each 20 years
of age.

(37). What is the probability that exactly four (4) of these six friends will live to reach the age of 65?
(A)0.306 (B)0.554 (C)0.108 (D)0.429 (E)0.246 (F)0.333 (G)0.404 (H)0.500 (I)0.275 (J)0.667

(38). What is the probability that at least five of these six friends will live to reach the age of 65?
(A)0.234 (B)0.587 (C)0.375 (D)0.451 (E)0.619 (F)0.556 (G)0.486 (H)0.262 (I)0.655 (J)0.393

Now suppose, for questions (39) and (40), that there are 150 students aged 20 in a large class.

(39). For such a group of 150 20-year-olds, determine the mean and standard deviation of the number within the group who can be expected to live at least until the age of 65 years. What s the product of these two values?
(A)747 (B)393 (C)426 (D)588 (E)622 (F)707 (G)532 (H)485 (I)350 (J)656

(40). What is the probability that, of the 150 twenty-year-olds involved, at least 115 of them will live to see their 65th birthdays?
(A)0.6314 (B)0.2737 (C)0.2263 (D)0.3636 (E)0.4118 (F)0.8686 (G)0.4356 (H)0.7737 (I)0.5882 (J)0.1314

#### Solution Preview

In some countries, girls are valued much less than boys. Sometimes women in such countries abort fetuses known to be girls and many girl babies are victims of infanticide. Suppose there are 43 girls to every 57 boys who reach age 1 in one such country.

The probability of having a girl over age 1 is
The probability of having a boy over age 1 is
(10). What is the probability that a family with three children (all over 1 year of age) has 2 boys and 1 girl?
You can think this is a binominal distribution. with n=3, and p= 0.57. Now k=2. The probability is

G is correct.

(11). What is the probability that this family will have at least 2 boys?
Same as the above, the probability of having 2 boys is
The probability of having 3 ...

#### Solution Summary

It provides examples of calculating the probability when the sample follows binominal distribution. The solution is detailed and has a '5/5' rating.

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