##### STA2023 STATISTICS

The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?

Number_of_girls P(x)

0 0.125

1 0.375

2 0.375

3 0.125

**Answer**.The random variable is x, which is the number
of girls in three births. The possible values of x are 0, 1, 2, and
3. The values of the random value x are numerical.

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation.

x P(x)

0 0.2373

1 0.3955

2 0.2637

3
0.0879

4 0.0146

5 0.0010

**Answer:**

m=1.3

random variable x=1

ed is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of girls Ted approaches before encountering one who reacts positively. Determine whether the table describes a probability distribution. If itdoes, find its mean and standard deviation.

x P(x)

1 0.002

2 0.033

3 0.138

4 0.216

5 0.402

**Answer:**

**
**

The table is not a probability distribution.

Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.47. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of threegirls?

x P(x)

0 0.149

1 0.396

2 0.351

3 0.104

**Answer:**

1. Find the mean of the random variable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- Mean=1.41

2. Find the standard deviation of the random variable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- SD=.86

3. Is it unusual for a family with three children to have only girls?

- No, because the probability of having 3 girls is greater than greater than 0.05.