Acorn Production

Suppose that the number of acorns that fall from a mature white oak tree in Bayfield County is strongly right-skewed with a mean of 875 and a standard deviation of 220.

  • What is an individual?
  • What is the variable?
  • What are the appropriate symbols for the 875 and 220?
  • Which distribution is strongly right-skewed?


I urge you to follow these steps when answering probability questions:
  1. Identify the distribution that would be used to answer the question (population or sampling).
  2. Identify characteristics of the required distribution; i.e., whether normal or not and, if normal, the center and dispersion (SD or SE).
  3. Identify whether the question can be answered or not (can be if normal, cannot be if not normal).
  4. Answer the question (see next box).
In all of the following questions, ...
  1. if the question can be answered then show a quick drawing that illustrates your calculation and the distrib() code used to compute the answer.
  2. If the probability cannot be computed then explain why not (and be specific about which distribution is not normal).


  1. What is the probability that a sample of 50 oak trees will produce a mean of more than 900 acorns?
  2. What is the probability that a sample of 35 oak trees will produce a mean between 850 and 900 acorns?
  3. What is the probability that an oak tree produces more than 1000 acorns?
  4. What is the probability that a sample of 20 oak trees will produce a mean with fewer than 1000 acorns?
  5. What is the mean number of acorns for a sample of 35 oak trees that has a 15% probability of the mean being greater.