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[4H-16] A bottle of orange juice is being filled by machine. Amount dispensed by the machine is known to be approximately normally distributed with mean of 10 ounces and standard deviation of m ounces. If we want to make sure that proportion of the bottles filled over 12 ounces to be 10%, what does the value of m have to be? (Round to 2 decimals.)

Respuesta :

Answer:1.5625

Step-by-step explanation:

Given

mean [tex]\mu =10 ounces[/tex]

standard deviation [tex]\sigma =m ounces [/tex]

For bottles to be filled over 12 ounces i.e. area right to the bell curve for z score

and area left  side of the z score is 1-0.1=0.9

so value close to 0.9 in standard normal curve which is  0.8997

z score corresponding to 0.8997 is 1.28

also z score for 12 ounce

[tex]z=\frac{x-\mu }{\sigma }[/tex]

[tex]z=\frac{12-10}{m}[/tex]

[tex]1.28=\frac{2}{m}[/tex]

[tex]m=\frac{2}{1.28}[/tex]

[tex]m=1.5625[/tex]

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