Step 1 :We are given a random sample of 45 individuals who consider themselves to be avid Internet users. The mean time they spend watching television on a weekday is 1.94 hours. We are asked to determine the likelihood of obtaining a sample mean of 1.94 hours or less from a population whose mean is presumed to be 2.35 hours.
Step 2 :To solve this, we first need to calculate the z-score. The z-score is a measure of how many standard deviations an element is from the mean. We can calculate it using the formula \( z = \frac{{\text{{sample mean}} - \text{{population mean}}}}{{\text{{population mean}} / \sqrt{{\text{{sample size}}}}}} \).
Step 3 :Substituting the given values into the formula, we get \( z = \frac{{1.94 - 2.35}}{{2.35 / \sqrt{45}}} \).
Step 4 :The calculated z-score is approximately -1.17.
Step 5 :Next, we use the cumulative distribution function (CDF) of the normal distribution to find the probability associated with this z-score. This probability represents the likelihood of obtaining a sample mean of 1.94 hours or less.
Step 6 :The corresponding probability is approximately 0.121.
Step 7 :So, the likelihood of obtaining a sample mean of 1.94 hours or less from a population whose mean is presumed to be 2.35 hours is \(\boxed{0.1210}\).