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.
I Will Do On Later!
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.