Question

Suppose a brewery has a filing machine that is 12 ounce bottles of beer, it is known that the amount of beer poured by this filing machine follows a normal dutiniowa mean of 12.10 and a standard deviation of .05 ounce. Find the probability that the bottle contains between 12.00 and 12.06 ounces

Answer 1

Let X be the random variable representing the amount of beer poured by the filling machine. Since X follows a normal distribution with mean μ = 12.10 and standard deviation σ = 0.05, we can use the standard normal distribution to find the probability that a bottle contains between 12.00 and 12.06 ounces.

First, we need to standardize the values 12.00 and 12.06 by subtracting the mean and dividing by the standard deviation:

z1 = (12.00 - 12.10) / 0.05 = -2 z2 = (12.06 - 12.10) / 0.05 = -0.8

Now we can use a standard normal distribution table to find the probability that a standard normal random variable Z is between -2 and -0.8:

P(-2 < Z < -0.8) = P(Z < -0.8) - P(Z < -2) ≈ 0.2119 - 0.0228 ≈ 0.1891

So, the probability that a bottle contains between 12.00 and 12.06 ounces of beer is approximately 0.1891.

Explanation: