Question

A soda production company fills cans that hold 12 ounces of soda. The actual amount of soda dispensed into each can is normally distributed with a mean of 11.9 oz. and a standard deviation of 0.02 oz. Use a calculator to find the probability that you find a can of soda with less than 11.87 oz.(1 point)
Responses

50%
50%

93.3%
93.3%

6.7%
6.7%

37.2%

Answer 1

To find the probability that a can of soda contains less than 11.87 ounces, we need to use the properties of the normal distribution.

The parameters given are:
- Mean (μ) = 11.9 ounces
- Standard deviation (σ) = 0.02 ounces

We want to find the probability \( P(X < 11.87) \).

First, we calculate the z-score for 11.87 ounces using the formula:

\[
z = \frac{X - \mu}{\sigma}
\]

Substituting in the values:

\[
z = \frac{11.87 - 11.9}{0.02} = \frac{-0.03}{0.02} = -1.5
\]

Next, we can use the z-score to find the probability. We look up the z-score of -1.5 in the standard normal distribution table or use a calculator for the cumulative distribution function (CDF).

Using a standard normal distribution table or calculator, we find:

\[
P(Z < -1.5) \approx 0.0668
\]

Thus, the probability of finding a can of soda with less than 11.87 ounces is approximately 6.68%, which can be rounded to about 6.7%.

Therefore, the correct response is:

**6.7%**