The average amount of time people spend on facebook each day is 71 minutes, with a standard deviation of 4.7 minutes. Are you more likely to select a random person that spends less than 68 minutes per day, or a group of 35 people that spend on average less than 65 minutes per day on facebook? Assume this is normally distributed. Find the chances of each to decided which is more likely by how much.

For the individual,

Z = (score-mean)/SD

For the group,

Z = (score-mean)/SEm

SEm = SD/√n

For both, find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

To answer this question, we can use the concept of z-scores and the standard normal distribution.

First, let's calculate the z-score for a person who spends less than 68 minutes per day. The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the value we want to compare (68 minutes), μ is the mean (71 minutes), and σ is the standard deviation (4.7 minutes).

z = (68 - 71) / 4.7
z ≈ -0.6383

Using a z-table or a calculator, we can find that the probability of selecting a person who spends less than 68 minutes per day on Facebook is approximately 0.2632 (26.32%).

Next, let's calculate the z-score for a group of 35 people who spend on average less than 65 minutes per day. For a group mean, the standard deviation is given by:

σ(group) = σ / √n

where n is the number of individuals in the group (35).

σ(group) = 4.7 / √35
σ(group) ≈ 0.793

Now, we calculate the z-score for the group mean of 65 minutes:

z = (x - μ) / σ(group)
z = (65 - 71) / 0.793
z ≈ -7.573

Again, using a z-table or a calculator, we find that the probability of selecting a group of 35 people who spend on average less than 65 minutes per day on Facebook is extremely close to 0% (approximately 0.000000001%).

Comparing the probabilities, we can conclude that you are more likely to select a random person who spends less than 68 minutes per day on Facebook than a group of 35 people who spend on average less than 65 minutes per day. The difference in probabilities is significant, with the individual having a probability of 26.32% and the group having a probability of almost 0%.