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?
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 your 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 central limit theorem and the properties of the sample mean.
Step 1: Calculate the standard error of the sample mean:
The standard error of the sample mean (SE) is calculated using the formula:
SE = σ / √n
Where σ is the standard deviation of the population (90.57) and n is the sample size (25).
SE = 90.57 / √25
SE = 90.57 / 5
SE = 18.11
Step 2: Calculate the z-score:
The z-score is a measure of how many standard errors the sample mean is away from the population mean. It is calculated using the formula:
z = (x - μ) / SE
Where x is the sample mean (190), μ is the population mean (175.5), and SE is the standard error.
z = (190 - 175.5) / 18.11
z = 14.5 / 18.11
z = 0.8
Step 3: Find the probability:
To find the probability of a z-score of 0.8 or greater, we can use a standard normal distribution table or a calculator. Using a table or calculator, we can find that the probability corresponding to a z-score of 0.8 is approximately 0.7881 (or 78.81%).
Therefore, 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%.