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Travka [436]
2 years ago
10

A machine that fills bottles on an assembly line does so according to a normal distribution, where the mean amount of liquid pou

red 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?
Mathematics
1 answer:
Whitepunk [10]2 years ago
6 0

Answer:

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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