Question

bottles filled by a certain machine are supposed to contain 12 oz of liquid. the fill volume is a random variable with a mean of 12.01 oz and a standard deviation of 0.2 oz. (a) what is the probability that a randomly selected bottle contains a volume less than 12 oz? step by step

Answer 1

The probability that a randomly selected bottle contains less than 12 oz is found by calculating the z-score (-0.25) and then finding the corresponding probability (40.13%) from the standard normal distribution.

Step-by-step explanation:

To calculate the probability that a randomly selected bottle contains a volume less than 12 oz, we need to use the standard normal distribution.

Given that the fill volume has a mean (μ) of 12.01 oz and a standard deviation (σ) of 0.2 oz, we first calculate the z-score for the volume we are interested in (12 oz).

The z-score is calculated by subtracting the mean from the value of interest and then dividing by the standard deviation: z = (X - μ) / σ. In this case, z = (12 - 12.01) / 0.2 = -0.05 / 0.2 = -0.25

Next, we look up the corresponding probability for the z-score in the standard normal distribution tables or use a calculator with statistical functions.

The z-score of -0.25 corresponds to a probability of approximately 0.4013. Therefore, there is a 40.13% chance that a randomly selected bottle contains less than 12 oz of liquid.