Question

In Exercises 15–20, refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.

Using Probabilities for Significant Events

a. Find the probability of getting exactly 1 girl in 8 births.

b. Find the probability of getting 1 or fewer girls in 8 births.

c. Which probability is relevant for determining whether 1 is a significantly low number ofgirls in 8 births: the result from part (a) or part (b)?

d. Is 1 a significantly low number of girls in 8 births? Why or why not?

Number of girls x	P(x)
0	0.004
1	0.031
2	0.109
3	0.219
4	0.273
5	0.219
6	0.109
7	0.031
8	0.004

Short answer

a. The probability of getting exactly 1 girl in 8 births is 0.031.

b. The probability of getting 1 or fewer girls in 8 births is 0.035.

c. The probability used in (b) part.

d. Yes, 1 is a significantly low number of girls in 8 births

Step-by-step solution

Given information

The probability distribution for the number of girls among 8 children is provided.

The variable x is the number of girls among 8 children.

Calculate the probability of getting exactly 1 girl in 8 births

a.

Using the probability distribution table, the probability corresponding to 6 girls in 8 births is 0.031.

Thus, the probability of getting exactly 1 girl in 8 births is 0.031.

Calculate the probability of getting 1 or fewer girls in 8 births

b.

Using the probability distribution table, the probability corresponding to 1 girl in 8 births is 0.031.

The probability corresponding to 0 girls in 8 births is 0.031.

The probability of getting 1 or fewer girls in 8 births is computed as:

$$\begin{gathered} P\left(x⩽1\right)=P\left(x=0\right)+P\left(x=1\right) \\ =0.004+0.031 \\ =0.035 \end{gathered}$$

Thus, the probability of getting 1 or fewer girls in 8 births is 0.035.

State the probability relevant to determine whether 1 is a low number of girls in 8 births

c.

The following probability expression is used to determine if the given sample value is significantly low or not:

$P\left(x\text{or}\text{fewer}\right)⩽0.05$

If the above expression holds true, then the number of successes for that event can be considered significantly low.

Here, part (b) computes the probability of 1 or fewer girls in 8 births.

The probability computed in (b) part is relevant to determine whether 1 is a low number of girls in 8 births.

Check whether 1 is a significantly low number of girls in 8 births

d.

Since the probability of 1 or fewer number of girls in 8 births is 0.035, which is less than 0.05, thus, the number of girls equal to 1 can be considered significantly low.