Question

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?

Answer 1

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

     $P( Z > 3.33 ) = 0.0004$

=>  $P( X > 12.10 ) =0.0004$