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Sagot :
Remember that on a normal distribution, 95% of the cases fall between an interval of radius 2 times the standard deviation around the mean. This is, 95% of the cases are inside the interval:
[tex]\lbrack\bar{x}-2\sigma,\bar{x}+2\sigma\rbrack[/tex]If the mean is equal to 1.4 and the standard deviation is 1.2, then:
[tex]\begin{gathered} \bar{x}-2\sigma=1.4-2(1.2) \\ =-1 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}+2\sigma=1.4+2(1.2) \\ =3.8 \end{gathered}[/tex]Observe that it is not possible for a student to have less than 0 siblings. Then, the cases in the interval [-1,0) are not real-life cases.
Mathematically, the answer would be:
[tex]\lbrack-1,3.8\rbrack[/tex]Which is the interval of 95% confidence for a normal distribution with mean 1.4 and standard deviation of 1.2
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