The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

plug in your data here ....

http://davidmlane.com/hyperstat/z_table.html

to get .4013

0.4013

To find the probability that the volume of soda in a randomly selected bottle is less than 32 oz, we can use the standard normal distribution.

Step 1: Calculate the z-score. The z-score is calculated as (X - μ) / σ, where X is the value we are interested in (32 oz in this case), μ is the mean (32.3 oz), and σ is the standard deviation (1.2 oz).

z-score = (32 - 32.3) / 1.2 = -0.25 / 1.2 = -0.208

Step 2: Use the z-score to find the probability using a standard normal distribution table or a calculator. The probability of getting a z-score less than -0.208 is the same as the probability of getting a value less than 32 oz.

Looking up the z-score in the standard normal distribution table or using a calculator, you can find that the probability corresponding to a z-score of -0.208 is approximately 0.417.

Therefore, the probability that the volume of soda in a randomly selected bottle will be less than 32 oz is approximately 0.417, or 41.7%.

To find the probability that the volume of soda in a randomly selected bottle will be less than 32 oz, we can use the concept of the standard normal distribution.

1. Convert the given values into a standard normal distribution:
- Calculate the z-score using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation.
- In this case, x = 32, μ = 32.3, and σ = 1.2.
- Calculate the z-score: z = (32 - 32.3) / 1.2

2. Look up the z-score in the standard normal distribution table.
- The standard normal distribution table provides the corresponding probability for each z-score.
- Locate the z-score from step 1 in the table and find the corresponding probability.

3. Interpret the result.
- The probability we find represents the likelihood of randomly selecting a soda bottle with a volume less than 32 oz.

Now let's calculate the probability:

1. Calculate the z-score:
z = (32 - 32.3) / 1.2
z = -0.25

2. Look up the z-score in the standard normal distribution table.
From the table or using a calculator, we find that the probability (area under the curve) to the left of z = -0.25 is approximately 0.4013.

3. Interpret the result:
The probability that the volume of soda in a randomly selected bottle will be less than 32 oz is approximately 0.4013 or 40.13%.

Therefore, the probability is approximately 0.4013 or 40.13%.