Question

3) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is
known that the amount of beer poured by this filling machine follows a normal
distribution with a mean of 12.14 ounces and a standard deviation of 0.06 ounce.
a) Find the probability that the bottle contains fewer than 12.00 ounces of beer.
Label the sketch of the normal curve with the values from the problem
situation. Label the mean and the desired outcome. Use a z-score to find the
probability. Round your answer to 2 decimal places.
b) Now that you have a probability that a bottle contains less than 12 ounces,
what would be the probability that at least one bottle in a six pack would
contain less than 12 ounces. Recall the probability of at least one from section
5-3, and a binomial distribution.
c) The brewery is concerned about the probability of a customer getting a bottle with
less than 12 ounces. What could the brewery do that would lower the chance that
a customer would get a bottle with less than 12 ounces?

Answer 1

This is a normal distribution question with

P(x < 12.0)=?
The z-score at x = 12.0 is,

z = -2.3333
This implies that
= 0.01
PS: you have to refer z score table to find the final probabilities.


This is a binomial distribution question with
n = 6
p = 0.0098
q = 1 - p = 0.9902
where



c) We can increase the average amount of beer that is filled in the bottle or try to decrease the standard deviation associated.


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