Facebook reports that the average number of facebook friends worldwide is 175.5 with the stand deviation of 90.57. Take sample of 25 students, what is the probability that the mean number Facebook friends in the sample will be 190 friends or more..HELP
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score. Multiply by 25.
You do not need to multiply by 25.
To find the probability that the mean number of Facebook friends in a sample of 25 students will be 190 friends or more, we can use the Central Limit Theorem and convert the problem into a standard normal distribution.
The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution.
First, let's calculate the standard error, which is the standard deviation of the sample means (also known as the standard deviation of the sampling distribution):
Standard error (SE) = Standard deviation (σ) / √(Sample size)
SE = 90.57 / √(25)
SE = 90.57 / 5
SE = 18.114
Next, we need to convert the sample mean of 190 into a z-score. The formula for calculating a z-score is:
z = (X - μ) / SE
Where X is the value you want to find the probability for, μ is the population mean, and SE is the standard error.
z = (190 - 175.5) / 18.114
z = 14.5 / 18.114
z ≈ 0.800
Now, we need to find the probability of having a z-score of 0.800 or more. We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table or calculator, we can find that the probability of having a z-score of 0.800 or more is approximately 0.2119.
Therefore, the probability that the mean number of Facebook friends in the sample will be 190 friends or more is approximately 0.2119, or 21.19%.