Facebook reports that the average number of Facebook friends worldwide is 175.5 with a standard deviation of 90.57. If you were to take a sample of 25 students, what is the probability that the mean number Facebook friends in the sample will be 190 friends or more?
You are dealing with a distribution of means.
Z = (score-mean)/SEm
SEm = SD/√n
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.
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 concept of the sampling distribution of the mean.
First, we need to calculate the standard error of the mean, which represents the standard deviation of the sample mean. The formula for the standard error is:
Standard Error (SE) = Standard Deviation (σ) / √sample size (n)
In this case, the standard deviation (σ) is given as 90.57, and the sample size (n) is 25. Let's calculate the standard error:
SE = 90.57 / √25 ≈ 18.11
Next, we need to convert the mean number of Facebook friends (190) into a z-score to find its corresponding probability. The z-score tells us how many standard errors away from the mean a particular value is.
The formula for calculating the z-score is:
z = (x - μ) / SE
Where x is the value we are interested in (190), μ is the population mean (175.5), and SE is the standard error (18.11). Let's calculate the z-score:
z = (190 - 175.5) / 18.11 ≈ 0.80
Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 0.80.
Looking up the z-score of 0.80 in a standard normal distribution table, we find that the corresponding probability is approximately 0.7881.
So, the probability that the mean number of Facebook friends in a sample of 25 students will be 190 friends or more is approximately 0.7881, or 78.81%.