Question

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.

Answer 1

Answer:

$z= \frac{2.1-1.98}{0.08}= 1.5$

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

$P(z>1.5)= 1-P(Z$

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:

$\mu = 1.98, \sigma =\sqrt{0.0064}= 0.08$

And we want to find this probability:

$P(X> \mu +1.5 \sigma = 1.98 +1.5*0.08 =2.1)$

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

$z=\frac{X -\mu}{\sigma}$

And replacing we got:

$z= \frac{2.1-1.98}{0.08}= 1.5$

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

$P(z>1.5)= 1-P(Z$

And the best answer would be:

C 0.07