Questions: The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below. B. Since the probability of getting 1 girl is the result from part (a), this is the relevant probability. C. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant D. Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant prob d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event. A. Yes, since the appropriate probability is less than 0.05 , it is a significantly low number. B. Yes, since the appropriate probability is greater than 0.05 , it is a significantly low number. C. No, since the appropriate probability is greater than 0.05 , it is not a significantly low number. D. No, since the appropriate probability is less than 0.05 , it is not a significantly low number. Number of Girls x P(x) 0 0.002 1 0.005 2 0.114 3 0.239 4 0.280 5 0.239 6 0.114 7 0.005 8 0.002

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below.

B. Since the probability of getting 1 girl is the result from part (a), this is the relevant probability.
C. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant
D. Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant prob
d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
A. Yes, since the appropriate probability is less than 0.05 , it is a significantly low number.
B. Yes, since the appropriate probability is greater than 0.05 , it is a significantly low number.
C. No, since the appropriate probability is greater than 0.05 , it is not a significantly low number.
D. No, since the appropriate probability is less than 0.05 , it is not a significantly low number.

Number of Girls x  P(x)
0  0.002
1  0.005
2  0.114
3  0.239
4  0.280
5  0.239
6  0.114
7  0.005
8  0.002
Transcript text: The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below. B. Since the probability of getting 1 girl is the result from part (a), this is the relevant probability. C. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant D. Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant prob d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event. A. Yes, since the appropriate probability is less than 0.05 , it is a significantly low number. B. Yes, since the appropriate probability is greater than 0.05 , it is a significantly low number. C. No, since the appropriate probability is greater than 0.05 , it is not a significantly low number. D. No, since the appropriate probability is less than 0.05 , it is not a significantly low number. \begin{tabular}{c|c} \hline \begin{tabular}{c} Number of \\ Girls $\boldsymbol{x}$ \end{tabular} & $\mathbf{P}(\mathbf{x})$ \\ \hline 0 & 0.002 \\ \hline 1 & 0.005 \\ \hline 2 & 0.114 \\ \hline 3 & 0.239 \\ \hline 4 & 0.280 \\ \hline 5 & 0.239 \\ \hline 6 & 0.114 \\ \hline 7 & 0.005 \\ \hline 8 & 0.002 \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Probability of Getting 1 Girl

The probability of having exactly 1 girl among 8 births is given by:

\[ P(X = 1) = 0.005 \]

Step 2: Probability of Getting More Than 1 Girl

The probability of having more than 1 girl is calculated as the sum of the probabilities of having 2, 3, 4, 5, 6, 7, or 8 girls:

\[ P(X > 1) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.993 \]

Step 3: Probability of Getting 0 Girls

The probability of having no girls at all is:

\[ P(X = 0) = 0.002 \]

Step 4: Significance of 1 Girl

To determine if having 1 girl is significantly low, we compare the probability \( P(X = 1) \) to the significance level \( \alpha = 0.05 \):

Since \( P(X = 1) = 0.005 < 0.05 \), we conclude that having 1 girl is significantly low.

Final Answer

The results are summarized as follows:

  • Probability of getting 1 girl: \( P(X = 1) = 0.005 \)
  • Probability of getting more than 1 girl: \( P(X > 1) = 0.993 \)
  • Probability of getting 0 girls: \( P(X = 0) = 0.002 \)
  • Conclusion: Yes, since the appropriate probability is less than 0.05, it is a significantly low number.

Thus, the final answer is:

\[ \boxed{Yes} \]

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