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 percentage of bottles contain less than 32 oz of soda?
Use same method.
0.4013
To find the percentage of bottles that contain less than 32 oz of soda, we can use the normal distribution and the given mean and standard deviation.
First, we need to standardize the value of 32 oz using the z-score formula:
z = (x - μ) / σ
where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.
Substituting the given values:
z = (32 - 32.3) / 1.2 = -0.25
Now, we need to find the area to the left of this value on the standard normal distribution table, which represents the percentage of bottles containing less than 32 oz.
Using the z-score table or a calculator, we can find that the area to the left of z = -0.25 is 0.4013.
Therefore, approximately 40.13% of bottles contain less than 32 oz of soda.
To find the percentage of bottles that contain less than 32 oz of soda, we need to calculate the area under the normal distribution curve to the left of 32 oz.
We can start by converting the values to a standardized form, using the formula: z = (X - μ) / σ, where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, we want to standardize 32 oz, with a mean of 32.3 oz and a standard deviation of 1.2 oz:
z = (32 - 32.3) / 1.2 = -0.25
Next, we can use a standard normal distribution table or a calculator to find the area to the left of z = -0.25.
Using a standard normal distribution table or a calculator, we can find that the area to the left of z = -0.25 is approximately 0.4013.
Thus, approximately 40.13% of bottles contain less than 32 oz of soda.