Question

Trade kings produces many types of soft drinks, including orange cola. the filling machines are adjusted to pour 12 ounces of soda into each 12-ounce can of orange cola. however, the actual amount of soda poured into each can is not exactly 12 ounces; it varies from can to can. it has been observed that the net amount of soda in such a can has a normal distribution with a mean of 12 ounces and a standard deviation of .015 ounce.

(i) what is the probability that a randomly selected can of orange cola contains 11.97 to 11.99 ounces of soda?

Answer 1

To find the probability, convert the values to z-scores, use the standard normal distribution table to find cumulative probabilities, and subtract the probabilities to get the desired range. The probability is approximately 0.386, or 38.6%.

Step-by-step explanation:

To find the probability that a randomly selected can of orange cola contains 11.97 to 11.99 ounces of soda, we need to convert the values to z-scores and use the standard normal distribution table.

The z-score for 11.97 ounces is (11.97 - 12) / 0.015 = -2, and the z-score for 11.99 ounces is (11.99 - 12) / 0.015 = -1.33.

The area under the standard normal curve between -2 and -1.33 represents the probability of a randomly selected can containing 11.97 to 11.99 ounces of soda.

To find this probability, we subtract the cumulative probability for -1.33 (0.4082) from the cumulative probability for -2 (0.0228). This gives us a probability of approximately 0.386.

Therefore, the probability that a randomly selected can of orange cola contains 11.97 to 11.99 ounces of soda is 0.386, or 38.6%