the accompanying table describes results from groups of 10 births from 10 different sets of parents. the…

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 8.2 girls (round to one decimal place as needed.) the minimum value in this range is girls (round to one decimal place as needed.) probability distribution for x number of girls x p(x) 0 0.003 1 0.016 2 0.039 3 0.115 4 0.207 5 0.245 6 0.196 7 0.116 8 0.043 9 0.014 10 0.004

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 8.2 girls (round to one decimal place as needed.) the minimum value in this range is girls (round to one decimal place as needed.) probability distribution for x number of girls x p(x) 0 0.003 1 0.016 2 0.039 3 0.115 4 0.207 5 0.245 6 0.196 7 0.116 8 0.043 9 0.014 10 0.004

Answer

Explanation:

Step1: Recall range - rule - of - thumb

The range - rule - of - thumb for significant values is $\mu\pm2\sigma$. First, find the mean $\mu$ and standard deviation $\sigma$ for a binomial distribution. For a binomial distribution $X\sim B(n,p)$, the mean $\mu = np$ and the standard deviation $\sigma=\sqrt{np(1 - p)}$. In the case of the number of girls in 10 births, $n = 10$ and assuming $p=0.5$ (probability of a girl in a single birth).

Step2: Calculate the mean

$\mu=np=10\times0.5 = 5$

Step3: Calculate the standard deviation

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

Step4: Find the lower limit of the non - significant range

The lower limit of the non - significant range is $\mu - 2\sigma=5-2\times1.58=5 - 3.16 = 1.8$

Answer:

$1.8$