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.)

Question

Accepted Answer

# Explanation:
## Step1: Calculate the mean
The formula for the mean of a probability - distribution is $\mu=\sum xP(x)$.
$$
\begin{align*}
\mu&=(0\times0.001)+(1\times0.013)+(2\times0.036)+(3\times0.116)+(4\times0.196)+(5\times0.234)+(6\times0.207)+(7\times0.113)+(8\times0.043)+(9\times0.017)+(10\times0.024)\
&=0 + 0.013+0.072 + 0.348+0.784+1.17+1.242+0.791+0.344+0.153+0.24\
&=5.157\approx5.2
\end{align*}
$$
## Step2: Calculate the variance
The formula for the variance is $\sigma^{2}=\sum(x - \mu)^{2}P(x)$.
$$
\begin{align*}
\sigma^{2}&=(0 - 5.2)^{2}\times0.001+(1 - 5.2)^{2}\times0.013+(2 - 5.2)^{2}\times0.036+(3 - 5.2)^{2}\times0.116+(4 - 5.2)^{2}\times0.196+(5 - 5.2)^{2}\times0.234+(6 - 5.2)^{2}\times0.207+(7 - 5.2)^{2}\times0.113+(8 - 5.2)^{2}\times0.043+(9 - 5.2)^{2}\times0.017+(10 - 5.2)^{2}\times0.024\
&=(27.04\times0.001)+(17.64\times0.013)+(10.24\times0.036)+(4.84\times0.116)+(1.44\times0.196)+(0.04\times0.234)+(0.64\times0.207)+(3.24\times0.113)+(7.84\times0.043)+(14.44\times0.017)+(23.04\times0.024)\
&=0.02704 + 0.22932+0.36864+0.56144+0.28224+0.00936+0.13248+0.36612+0.33712+0.24548+0.55296\
&=2.8812
\end{align*}
$$
## Step3: Calculate the standard deviation
The standard deviation $\sigma=\sqrt{\sigma^{2}}$, so $\sigma=\sqrt{2.8812}\approx1.7$
## Step4: Use the range rule of thumb
The range rule of thumb states that values are not significant if they are within $\mu\pm2\sigma$. The upper limit is $\mu + 2\sigma$.
Substitute $\mu = 5.2$ and $\sigma=1.7$ into $\mu + 2\sigma$: $5.2+2\times1.7=5.2 + 3.4=8.6$

# Answer:
$8.6$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the mean

Step2: Calculate the variance

Step3: Calculate the standard deviation

Step4: Use the range rule of thumb

Answer: