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. click the icon to view the table. 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.) the minimum value in this range is girls (round to one decimal place as needed.) based on the result, is 1 girl in 10 births a significantly low number of girls? explain. a. yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant. b. no, 1 girl is not a significantly low number of girls, because 1 girl is within the range of values that are not significant. c. yes, 1 girl is a significantly low number of girls, because 1 girl is above the range of values that are not significant. d. not enough information is given. probability distribution for x

number of girls x	p(x)
1	0.015
2	0.037
3	0.116
4	0.208
5	0.247
6	0.201
7	0.113
8	0.038
9	0.014
10	0.008

Explanation:

Step1: Recall the range - rule - of - thumb for significant values

The range - rule - of - thumb for significant low and high values in a binomial distribution is given by $\mu\pm2\sigma$. First, we need to find the mean $\mu$ and standard deviation $\sigma$ of the binomial distribution. For a binomial distribution $X\sim B(n,p)$, where $n = 10$ (number of trials, i.e., number of births) and assuming the probability of having a girl $p=0.5$ (since the probability of having a boy or a girl is approximately 0.5 in the absence of other factors), the mean $\mu=np$ and the standard deviation $\sigma=\sqrt{np(1 - p)}$.
$\mu=np=10\times0.5 = 5$
$\sigma=\sqrt{10\times0.5\times(1 - 0.5)}=\sqrt{10\times0.5\times0.5}=\sqrt{2.5}\approx1.58$

Step2: Calculate the non - significant range

The non - significant range is $\mu\pm2\sigma$.
Lower limit: $\mu - 2\sigma=5-2\times1.58=5 - 3.16 = 1.84\approx1.8$
Upper limit: $\mu + 2\sigma=5 + 2\times1.58=5+3.16 = 8.16\approx8.2$

Answer:

The maximum value in this range is 8.2 girls.
The minimum value in this range is 1.8 girls.
A. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant.