1) Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder.Determine whether a probability distribution is given.

x P(x)

0 0.0313

1 0.1562

2 0.3125

3 0.3125

4 0.1562

5 0.0313

a) Find the mean of the random variable x.

b) Find the standard deviation of the random variable x.

2) The accompanying table describes the results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.

x P(x)

0 0.0039

1 0.0313

2 0.1094

3 0.2188

4 0.2734

5 0.2188

6 0.1094

7 0.0313

8 0.0039

a) Find the mean of the number of girls in 8 births.

=

b) Find the standard deviation of the number of girls in 8 births.

=

c) Find the variance of the number of girls in 8 births.

=

3) Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consists of 29 couples, answer the following questions.

a) Find the mean for the number of girls in group of 29 births.

=14.5

b) Find the variance for the number of girls in group of 29 births.

^2 =7.25

c) Find the standard deviation for the number of girls in group of 29 births.

=

d) Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

Values of girls or fewer are significantly low.

Values of or greater are significantly high.

4) There is a 0.9987 probability that a randomly selected 30-year-old male lives through the year. A life insurance company charges $186 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $120,000 as a death benefit. Answer the following questions.

a) From the perspective of the 30-year-old male, what are the monetary values correspoding to the two events of surviving the year and not surviving?

The value corresponding to surviving the year is $