A soda factory has a special manufacturing line to fill large bottles with 2 liters of their beverage. Every process is computerized. However, it doesn't always fill exactly 2 liters. It follows a normal distribution, witha mean of 1.98 liters and a variance of 0.0064 liters. If the amount of soda in a bottle is more than 1.5 standard deviations away from the mean, then it will be rejected. Find the probability that a randomly selected bottle is rejected.
A 0
B 0.04
C 0.07
D 0.13
E 0.

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dfbustos dfbustos · Answer 1 · 2020-07-19T02:55:57+02:00

Answer:

[tex] z= \frac{2.1-1.98}{0.08}= 1.5[/tex]

And we can use the normal standard table and the complement rule and we got:

[tex]P(z>1.5)= 1-P(Z<1.5) =1- 0.933= 0.067 \approx 0.07[/tex]

And the best answer would be:

C 0.07

Step-by-step explanation:

Let X the random variable who represent the amount of soda filled in large bottles and we know this:

[tex]\mu = 1.98, \sigma =\sqrt{0.0064}= 0.08[/tex]

And we want to find this probability:

[tex] P(X> \mu +1.5 \sigma = 1.98 +1.5*0.08 =2.1)[/tex]

And for this case we can use the z score formula given by:

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

And replacing we got:

[tex] z= \frac{2.1-1.98}{0.08}= 1.5[/tex]

And we can use the normal standard table and the complement rule and we got:

[tex]P(z>1.5)= 1-P(Z<1.5) =1- 0.933= 0.067 \approx 0.07[/tex]

And the best answer would be:

C 0.07