A cola-dispensing machine is set to dispense a mean of 2.024 liters into a container labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.040 liters. What is the probability a container will have less than 2 liters?
0.0375
0.1614
0.4734
0.2743
Using this webpage you don't even have to find the z-scores (you may if you wish)
just enter the mean, the SD, click on "below" and enter 2 in that field and "recalculate"
to get .2743
http://davidmlane.com/hyperstat/z_table.html
perfect substitute for those terrible tables in the back of old textbooks
Thank you
To calculate the probability that a container will have less than 2 liters, we need to find the area under the normal distribution curve to the left of 2 liters.
Step 1: Standardize the value of 2 liters using the formula:
z = (x - μ) / σ
Where:
x = 2 liters (value we want to find the probability for)
μ = mean = 2.024 liters
σ = standard deviation = 0.040 liters
Substituting the values:
z = (2 - 2.024) / 0.040
z = -0.6
Step 2: Look up the corresponding z-value in the standard normal distribution table.
Using the table, a z-value of -0.6 corresponds to a cumulative probability of 0.2743.
Therefore, the probability that a container will have less than 2 liters is 0.2743.
The correct answer is: 0.2743
To solve this problem, we will use the concept of the z-score. The z-score allows us to standardize any given value in a normal distribution.
First, let's find the z-score for the value of 2 liters. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
x = given value (2 liters)
μ = mean (2.024 liters)
σ = standard deviation (0.040 liters)
z = (2 - 2.024) / 0.040
z = -0.6
Next, we need to find the probability of having less than 2 liters. Since we want the area to the left of 2 liters on a standard normal distribution curve, we need to find the cumulative probability up to that point.
Using a standard normal distribution table or a calculator, we can find that the cumulative probability for a z-score of -0.6 is approximately 0.2743.
Therefore, the answer is 0.2743.