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A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters. actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters. what is the probability a container will have less than 2 liters?

Respuesta :

JeanaShupp

Answer: 0.9087.

Step-by-step explanation:

Given  : Population mean : [tex]\mu=2.02\text{ liters}[/tex]

Standard deviation : [tex]\sigma =0.015\text{ liters}[/tex]

Here , the actual quantities dispensed vary and the amounts are normally distributed .

Let x be the amount of cola in container in liters :-

[tex]P(x<2)=P(\dfrac{x-\mu}{\sigam}<\dfrac{2-2.02}{0.015})\\\\=P(z<-1.33333)\ \ \ [\because\ z=\dfrac{x-\mu}{\sigma}}]\\\\= 0.9087\ \ [\text{Using P-value table}][/tex]

Thus , the probability a container will have less than 2 liters is 0.9087.

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