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A company that manufactures and bottles apple juice uses a machine that automatically fills 16–ounce bottles. There is some variation in the amounts of liquid dispensed into the bottles. The amount dispensed is approximately normally distributed with mean 16 ounces and standard deviation 1 ounce. What proportion of bottles will have more than 17 ounces?

Respuesta :

JeanaShupp

Answer:  0.1587

Step-by-step explanation:

Given : The amount dispensed is approximately normally distributed with Mean : [tex]\mu=\ 16[/tex]

Standard deviation : [tex]\sigma= 1[/tex]

The formula to calculate the z-score :-

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

For x= 17

[tex]z=\dfrac{17-16}{1}=1[/tex]

The p-value =[tex] P(17<x)=P(1<z)[/tex]

[tex]=1-P(z<1)=1-0.8413447\\\\=0.1586553\approx0.1587[/tex]

The proportion of bottles will have more than 17 ounces = 0.1587

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