Question

Soda cans A machine that fills cans with soda fills according to a Normal model with mean 12.1 ounces and standard deviation 0.05 ounces. a. If the cans claim to have 12 ounces of soda each, what percent of cans are under-filled

Answer 1

Answer:

The percentage is  $p = 4.55\%$

Step-by-step explanation:

From the question we are told that

 The mean is $\mu = 12.1 \ ounce$

  The standard deviation is  $\sigma = 0.05 \ ounce$

    The value of soda each can claims to have is  $X = 12 \ ounce$

Generally the z-score is mathematically represented  as

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

=>      $z = \frac{ 12-12.1 }{0.05}$

=>      $z = -2$

From the z table the area under the normal  curve representing the proportion of under filled cans is

      $P(x <-2 \ or\ x > 2)= 0.0455$

Converting to  percentage

       $p = 0.0455 *100$

=>    $p = 4.55\%$