Respuesta :
The probability that the average of four babies' weights will be within 1. 2 pounds of the mean; will be between 6. 8 and 9. 2 pounds is 0.74.
What is the probability?
Probability is the branch of mathematics, which discusses the occurrence of a random experiment.
The average of four babies' weights will be within 1. 2 pounds of the mean; will be between 6. 8 and 9. 2 pounds.
The standard error of the sample will be:
[tex]\rm Standard \ error=\dfrac{Standard deviation}{\sqrt{ Number \ of \ babies} }\\\\\rm Standard \ error=\dfrac{1.2}{\sqrt{ 4} }\\\\Standard \ error=\dfrac{1.2}{2}\\\\Standard \ error=0.6[/tex]
The probability that the average of four babies P(4 babies will be between 8.4 - 9.6 pounds) is;
[tex]\rm P(6.8\leq X\leq 9.2)= \left( \dfrac{6.8-8}{0.6}\leq X\leq \dfrac{9.2-8}{0.6} \right )\\\\\rm P(6.8\leq X\leq 9.2)= \left( \dfrac{-1.2}{0.6}\leq X\leq \dfrac{1.2}{0.6} \right )\\\\\rm P(6.8\leq X\leq 9.2)= \left( -2\leq X\leq 2 \right )\\\\\rm P(6.8\leq X\leq 9.2)= P(Z\leq -2)-P(Z\leq 2)\\\\ P(6.8\leq X\leq 9.2)=0.97-0.22\\\\ P(6.8\leq X\leq 9.2)=0.74[/tex]
Hence, the probability that the average of four babies' weights will be within 1. 2 pounds of the mean; will be between 6. 8 and 9. 2 pounds is 0.74.
Learn more about probability here;
https://brainly.com/question/17205926
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