Solve the problem.
-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 12.49 ounces and a standard
Deviation of 0.04 ounce. Find the probability that the bottle contains between 12.39 and 12.45 ounces.
A) 0.1649
B) 0.1525
C) 0.8351
D) 0.8475

Question

Quizplus · Accepted Answer

To find the probability that the bottle contains between 12.39 and 12.45 ounces, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 12.39 ounces, $Z = \frac{12.39 - 12.49}{0.04} = -2.5$, and for 12.45 ounces, $Z = \frac{12.45 - 12.49}{0.04} = -1$. Looking these Z-scores up in the standard normal distribution table gives us the probabilities of 0.0062 and 0.1587, respectively. The probability of being between these two values is the difference, 0.1587 - 0.0062 = 0.1525.

Solve the Problem. -Suppose a Brewery Has a Filling Machine That Fills 12