5 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 isa 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 5.1 girls.(Round to one decimal place as needed.)The minimum value in this range is 1.7 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,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. Number ofGirls xP(x)0.00310.0120.03630.11340.2060.2420.20470.11680.0420.012100.014

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Description: 5 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 isa si

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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.CR: Chapter Review

Problem 37E: Find the positive geometric mean between 4 and 64.

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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 5.1 girls.
(Round to one decimal place as needed.)
The minimum value in this range is 1.7 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,
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.

Number of
Girls x
P(x)
0.003
1
0.012
0.036
3
0.113
4
0.206
0.242
0.204
7
0.116
8
0.042
0.012
10
0.014

Expert Solution

Step 1

Given Information:

Using the range rule of thumb we are asked to determine the range of values that are not significant:

Using the above probability distribution table, find the mean and standard deviation as follows:

Mean/ Expected value:

$\begin{array}{rcl} μ & = & \sum_{i} x P (x) \\ = & 0 (0.003) + 1 (0.012) + 2 (0.036) + 3 (0.113) + 4 (0.206) + 5 (0.242) + 6 (0.204) + 7 (0.116) + 8 (0.042) + 9 (0.012) + 10 (0.014) \\ = & 5.077 \end{array}$

Standard deviation is calculated using the formula:

$σ = \sqrt{E (X^{2}) - {[E (X)]}^{2}}$

$\begin{array}{rcl} E (X^{2}) & = & \sum_{i} x^{2} P (x) \\ = & 0 (0.003) + 1 (0.012) + 4 (0.036) + 9 (0.113) + 16 (0.206) + 25 (0.242) + 36 (0.204) + 49 (0.116) + 64 (0.042) + 81 (0.012) + 100 (0.014) \\ = & 28.607 \end{array}$

Substitute the values in the above formula:

$\begin{array}{rcl} σ & = & \sqrt{E (X^{2}) - {[E (X)]}^{2}} \\ = & \sqrt{28.607 - {(5.077)}^{2}} \\ = & 1.682578676 \\ \approx & 1.6826 \end{array}$

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