Question

the accompanying table describes results from groups of 10 births from 10 different sets of parents. the random variable x represents the number of girls among 10 children. use the range - rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. use the range - rule of thumb to identify a range of values that are not significant. the maximum value in this range is girls (round to one decimal place as needed). probability distribution for x

number of girls x	p(x)
1	0.016
2	0.039
3	0.115
4	0.207
5	0.245
6	0.198
7	0.116
8	0.043
9	0.014
10	0.004

Explanation:

Step1: Calculate the mean

For a binomial distribution of \(n = 10\) (number of births) and assuming \(p=0.5\) (probability of a girl in a single - birth, since there are two equally likely genders), the mean \(\mu=np = 10\times0.5=5\).

Step2: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{np(1 - p)}=\sqrt{10\times0.5\times(1 - 0.5)}=\sqrt{10\times0.5\times0.5}=\sqrt{2.5}\approx1.58\).

Step3: Use the range - rule of thumb

The range - rule of thumb for significant values is \(\mu\pm2\sigma\). The maximum non - significant value is \(\mu + 2\sigma\). Substitute the values of \(\mu\) and \(\sigma\): \(5+2\times1.58=5 + 3.16 = 8.2\).

Answer:

8.2