Question

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

a)

µ =    12.14      
σ =    0.06      
          
P( X ≤    12   ) = P( (X-µ)/σ ≤ (12-12.14) /0.06)  
=P(Z ≤   -2.333   ) =   0.01

b)

Sample size , n =    6
Probability of an event of interest, p =   0.01

	X	P(X)
P ( X = 0) = C (6,0) * 0.01^0 * ( 1 - 0.01)^6=	0	0.9415

P(atleast 1) = 1- P(0)

= 1 - 0.9415

= 0.0585

c)

brewery should decrese the standard deviation (for which they have to incresed the sample size)

THANKS

revert back for doubt

please upvote