Question

The amount of water in a bottle is approximately normally distributed with a mean of 2.80 liters with a standard deviation of 0.045 liter. Complete parts​ (a) through​ (e) below.

Part 1

a. What is the probability that an individual bottle contains less than 2.76 liters?

Answer 1

The probability that an individual bottle contains less than 2.76 liters is approximately 18.67%.

Step-by-step explanation:

To find the probability that an individual bottle contains less than 2.76 liters, we need to standardize the value of 2.76 using the z-score formula. The z-score is calculated as (x - mean) / standard deviation, where x is the value we want to standardize, mean is the mean of the distribution (2.80 liters), and standard deviation is the standard deviation of the distribution (0.045 liter). Substituting the values, we get z = (2.76 - 2.80) / 0.045 = -0.89.

Next, we need to find the area under the standard normal distribution curve to the left of z = -0.89. We can use a standard normal distribution table or a calculator to find this area. Looking up the z-score -0.89 in the standard normal distribution table, we find that the corresponding area is approximately 0.1867. Therefore, the probability that an individual bottle contains less than 2.76 liters is approximately 0.1867 or 18.67%.