Find and Interpret the Area under a Normal Curve
-The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.18 ounce. The cans only hold 12.45 ounces of soda. Every can that has more than 12.45 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process
A) 0.1587
B) 0.3413
C) 0.8413
D) 0.6587

Question

Quizplus · Accepted Answer

To find the probability that a can will need to go through the special cleaning process, we calculate the z-score for 12.45 ounces using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X = 12.45$, $\mu = 12.27$, and $\sigma = 0.18$. This gives us $z = \frac{(12.45 - 12.27)}{0.18} = 1$. Looking up the z-score of 1 in the standard normal distribution table, we find that the area to the left of z=1 is 0.8413. Since we are interested in the area to the right (the probability of a can needing cleaning), we subtract this from 1, giving $1 - 0.8413 = 0.1587$. This means there's a 15.87% chance a can will overflow and need cleaning.

Find and Interpret the Area Under a Normal Curve