91Ó°ÊÓ

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

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

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.

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:

$$\begin{gathered} P\left(xâ\copyright ½1\right)=P\left(x=0\right)+P\left(x=1\right) \\ =0.004+0.031 \\ =0.035 \end{gathered}$$

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

c.

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

$P\left(x\text{or}\text{fewer}\right)â\copyright ½0.05$

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.

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.