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The amount of water in a bottle is approximately normally distributed with a mean of 2.10 liters with a standard deviation of 0.045 liter. What is the probability that an individual bottle contains less than 2.06 liters?

User Zah
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Final answer:

Using the Z-score formula and a standard normal distribution table, one can find the probability that a bottle of water with a normally distributed amount contains less than 2.06 liters, given the mean of 2.10 liters and a standard deviation of 0.045 liter.

Step-by-step explanation:

The student's question concerns finding the probability of a continuous random variable, specifically the amount of water in a bottle, being within a certain range when the variable follows a normal distribution. This falls under the area of statistics, which is a branch of mathematics. To find the probability that a bottle contains less than 2.06 liters when the amount of water is normally distributed with a mean (μ) of 2.10 liters and a standard deviation (σ) of 0.045 liter, one would use the Z-score formula:

Z = (X - μ) / σ

Where X is the value for which we are finding the probability (2.06 liters in this case). After calculating the Z-score, one would then refer to the standard normal distribution table to find the corresponding probability.

For the example of the bottle containing 2.06 liters, the calculation is as follows:

Z = (2.06 - 2.10) / 0.045 = -0.89

Using a standard normal distribution table, we can find the probability that corresponds to a Z-score of -0.89. This probability tells us how likely it is to have a bottle containing less than 2.06 liters of water.

User Nic Cottrell
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