Question

reported in 2014 that the mean number of Facebook friends for 18- to 24-year-olds is 649....

reported in 2014 that the mean number of Facebook friends for 18- to 24-year-olds is 649. Assume the distribution is normal with μ=649 friends and standard deviation σ=150 friends. Find the probability that a randomly selected Facebook user has the following number of friends:

  1. Fewer than 424 friends.
  2. More than 949 friends.
  3. Between 424 and 949 friends.
  4. Find the number of Facebook friends that represents the 75th percentile.
  5. One particular Facebook user has 1174 friends. Is this unusual? On what do you base your answer?
  6. A Facebook newbie has a number of friends equal to the 5th percentile. Find the 5th percentile of Facebook friends.
  7. An online socialite has the 95th percentile of friends. Compute the 95th percentile.
  8. Calculate the two symmetric numbers of friends X1 and X2 that contain the central 90% of Z-values between them. Is there a shortcut you can take?
  9. Calculate the two symmetric numbers of friends X1 and X2 that contain the central 95% of Z-values between them.
  10. What if we calculate the two symmetric numbers of friends that contain an unknown value greater than 95% between them? Will the values X1 and X2 be closer together or farther apart than the 95% case? Explain.
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