Cola Corporation produces Orange Cola. The filling machines are adjusted to pour 12 ounces of soda into each 12-ounce can. 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 0.015 ounce.

Question

Cola Corporation produces Orange Cola. The filling machines are adjusted to pour 12 ounces of soda into each 12-ounce can. 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 0.015 ounce.

a. What is the probability that a randomly selected can of Orange Cola contains between 11.97 to 11.99 ounces of soda?
b. What percentage of the Orange Cola cans contain 12.02 to 12.07 ounces of soda?

Answer 1

To solve these probability questions, we need to use the properties of the normal distribution. In this case, the mean (μ) is 12 ounces and the standard deviation (σ) is 0.015 ounce.

a. To find the probability that a randomly selected can contains between 11.97 and 11.99 ounces of soda, we can calculate the z-scores for these values and use a standard normal distribution table.

Using the z-score formula: z = (x - μ) / σ

For 11.97 ounces:
z1 = (11.97 - 12) / 0.015

For 11.99 ounces:
z2 = (11.99 - 12) / 0.015

Now, we can look up the probabilities corresponding to these z-scores in the standard normal distribution table. The table provides the cumulative probability up to a given z-score.

Let's assume the probability for z1 is P1 and the probability for z2 is P2.

The probability that a randomly selected can contains between 11.97 to 11.99 ounces of soda is given by:
P = P2 - P1

b. To find the percentage of Orange Cola cans containing 12.02 to 12.07 ounces of soda, we repeat the same steps by calculating the z-scores for these values and finding the cumulative probabilities.

Using the z-score formula:
For 12.02 ounces:
z3 = (12.02 - 12) / 0.015

For 12.07 ounces:
z4 = (12.07 - 12) / 0.015

Again, let's assume the probability for z3 is P3 and the probability for z4 is P4.

The percentage of Orange Cola cans containing 12.02 to 12.07 ounces of soda can be calculated as:
Percentage = (P4 - P3) * 100

To find the actual values of P1, P2, P3, and P4, you can use a standard normal distribution table or a statistical software program.

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To solve these probability questions, we need to use the properties of the normal distribution. In this case, the mean (μ) is 12 ounces and the standard deviation (σ) is 0.015 ounce.