Mathematics: A machine that fills bottles on an assembly line does so according to a normal distribution, where the mean amount of liquid poured into each bottle is 11.95 ounces with a standard deviation of 0.045 ounces. If more than 12.10 ounces is poured into a bottle, it will overflow and waste the liquid. Required: What is the probability that a bottle has more than 12.10 ounces poured into it, causing it to overflow?

A machine that fills bottles on an assembly line

Ответ:

arivalen

09.02.2022

Mathematics

The probability is P( X 12.10 ) =0.0004

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 11.95 \ ounce$

The standard deviation is $\sigma = 0.045 \ ounce$

Generally the probability that a bottle has more than 12.10 ounces poured into it, causing it to overflow is mathematically represented as

$P( X 12.10 ) = P( \frac{X - \mu }{\sigma } \frac{ 12.10 - 11.95}{0.045} )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

P( X 12.10 ) = P( Z 3.33 )

From the z table the area under the normal curve to the right corresponding to 3.33 is

P( Z 3.33 ) = 0.0004

=> P( X 12.10 ) =0.0004

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Ответ:

rmathias485

07.01.2022

Mathematics

I used the substitution method.
The first equation is what I used: y=-6x+9.7
So I plugged in y in the second equation.
4x + 2(-6x+9.7)= 9.8
4x-12x+19.4=9.8
Combine like terms
-8x+19.4=9.8
Subtract 19.4 on both sides
-8x=-9.6
Divide by -8 on both sides and you get
x=1.2
If you wanted to find y use either equation and plug in for x with the value of x!

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