Daily water intake (including water used in drinks such as coffee, tea and juice) for Canadian adults follows a normal distribution with mean $\var{mu}$ litres and standard deviation $\var{sigma}$ litres.

a) What is the probability that the mean daily water intake for a random sample of two Canadian adults is less than $\var{partaxbar}$ litres?

No numerical data.

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To find the probability that the mean daily water intake for a random sample of two Canadian adults is less than $\var{partaxbar}$ litres, we need to use the information about the normal distribution given by the mean ($\mu$) and the standard deviation ($\sigma$).

Let's assume that the random variable $X$ represents the mean daily water intake for a random sample of two Canadian adults. Since the problem states that this variable follows a normal distribution, we can write it as:

$$X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$$

where $\mu$ is the mean daily water intake for Canadian adults, $\sigma$ is the standard deviation, and $n$ is the sample size (which is 2 in this case).

Now we can calculate the probability using the standard normal distribution (z-distribution) and its cumulative distribution function (CDF). The CDF gives the probability that a normal random variable is less than or equal to a given value.

First, we need to calculate the z-score for $\bar{x}$ (the given mean daily water intake). The z-score formula is:

$$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$

Substituting the given values into the formula:

$$z = \frac{\var{partaxbar} - \mu}{\frac{\sigma}{\sqrt{2}}}$$

Next, we can use the z-score to find the probability using a standard normal distribution table or a calculator. The cumulative distribution function (CDF) gives the probability that $X$ is less than or equal to $\var{partaxbar}$.

$$P(X < \var{partaxbar}) = P\left(z < \frac{\var{partaxbar} - \mu}{\frac{\sigma}{\sqrt{2}}}\right)$$

Using the z-table or a calculator, we can find the corresponding probability for the z-score. This will give us the final answer to the question: the probability that the mean daily water intake for a random sample of two Canadian adults is less than $\var{partaxbar}$ litres.