The accompanying data table describes results from groups of 10 births from 10 d
ID: 3180782 • Letter: T
Question
The accompanying data 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. Complete the questions below.
x
P(x)
0
0.0040.004
1
0.0120.012
2
0.0430.043
3
0.1160.116
4
0.2020.202
5
0.2480.248
6
0.2010.201
7
0.1170.117
8
0.0370.037
9
0.0110.011
10
0.0090.009
Use the range rule of thumb to identify a range of values containing the usual numbers of girls in 10 births.
The maximum usual value is?
(Round to one decimal place as needed.)
The minimum usual value is?
(Round to one decimal place as needed.)
Based on the result, is 1 girl in 10 births an unusually low number of girls? Explain.
A.
Yes, 1 girl is an unusually low number of girls, because 1 girl is outside of the range of usual values.
B.
No, 1 girl is not an unusually low number of girls, because 1 girl is less than the minimum usual value.
C.
Yes, 1 girl is an unusually low number of girls, because 1 girl is less than the maximum usual value.
D.
Not enough information is given.
x
P(x)
0
0.0040.004
1
0.0120.012
2
0.0430.043
3
0.1160.116
4
0.2020.202
5
0.2480.248
6
0.2010.201
7
0.1170.117
8
0.0370.037
9
0.0110.011
10
0.0090.009
Explanation / Answer
Firstly we will find mean and sd of this probability distribution
In order to find the mean (expectation) of the given distribution, we will use the following formula:
=xp(x)=5.004
In order to find the standard deviation of the given distribution, we will use the following formula:
=(x2p(x)2)=1.6577
The range rule of thumb for the maximum usual value is given by the formula below, where and are the mean and standard deviation, respectively, for a probability distribution.
maximum usual value = + 2
so it is 5.004+2*1.6577=8.3194
minimum unsual value = – 2
so it is 5.004-2*1.6577=1.6886
Yes, 1 girl is an unusually low number of girls, because 1 girl is outside of the range of usual values.
Hence answer is A.
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