Statistics - Probability & z-score

In summary, the average time spent on Facebook per day is 64 minutes with a standard deviation of 4.5 minutes. The question is whether it is more likely to select one random person who spends less than 62 minutes per day or a group of 35 people who spend on average less than 62 minutes per day. The top 5% of Facebook users would have to spend how many minutes per day? The formula Z=X-M/SD may be helpful, but the number of people for the first experiment is not given. However, it is known that the sample size for the second experiment is 35.
  • #1
charr1010
2
0
The average amount of time people spend on facebook each day is 64 minutes, with a standard deviation of 4.5 minutes. Are you more likely to select a random person that spends less than 62 minutes per day, or a group of 35 people that spend on average less than 62 minutes per day on facebook? How many minutes would a person have to be on facebook to be considered the top 5%?


Z= X - M / SD

I am pretty sure this is the formula to use for this problem. I just got confused with what the number of people would be for the first half of the problem, the random person, because it is not given. If anyone can point me in the right direction it would be greatly appreciated. Thank you very much.
 
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  • #2
You are comparing two experiments. One has 35 people in it. How many does the other have in it?
 
  • #3
That lies the problem. What is written is all that is given for the problem and that is also why I am having such difficulty.
 
  • #4
If you pick 35 random people out of the population, the size of your sample is 35.
If you pick one random person out of the population, the size of your sample is... one.
 

1. What is the difference between probability and z-score?

Probability is the likelihood of a specific outcome occurring in a set of possible outcomes. It is expressed as a value between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Z-score, on the other hand, is a measure of how many standard deviations a data point is away from the mean of a dataset. It is used to standardize different datasets to allow for comparison.

2. How is the z-score calculated?

The z-score is calculated by subtracting the mean of the dataset from the data point and then dividing by the standard deviation. This formula is represented as z = (x - μ) / σ, where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.

3. What is a normal distribution and how is it related to z-scores?

A normal distribution is a bell-shaped curve that represents the distribution of data in a dataset. It is characterized by its mean and standard deviation and is used to describe many natural phenomena. Z-scores are used to standardize data and convert it into a standard normal distribution with a mean of 0 and a standard deviation of 1, making it easier to compare data from different datasets.

4. How is probability calculated using z-scores?

Probability can be calculated using z-scores by using a z-score table or a statistical software. The z-score represents the number of standard deviations a data point is away from the mean, and the z-score table gives the corresponding probability of that data point occurring. This probability can also be calculated using the standard normal distribution formula.

5. What is the significance of z-scores in hypothesis testing?

Z-scores play a crucial role in hypothesis testing as they allow for the calculation of p-values, which determine the statistical significance of a test. Z-scores are used to calculate the critical value, which is then compared to the p-value to determine whether to reject or fail to reject the null hypothesis. Z-scores also help in determining the effect size of a test, which measures the magnitude of the difference between the null and alternative hypotheses.

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