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Sampling distributions and random variables.

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It's 10 PM - do you know where your trash can is? In our neighborhood, there have been a varying number of black bear visits each year over the past six years. These visits usually result in a lot of late night noise and mess to clean up in the morning, as the black bears tip over the trash cans and dine on the contents. The number of these black bear visits each year since 2000 is shown below:

(see chart in attached file)
a. Let the random variable X = Number of Black Bear Visits per Year, and construct a probability distribution (table and chart) for this population, i.e. show X and P(X).

b. Construct the sampling distribution of the sample means (table and chart) for n = 2.
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c In words, what does the random variable, X, (X-bar) stand for in this problem.

d. Compute the mean of the sampling distribution; how does this compare with the population mean of the distribution in part a.
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Solution Summary

Sampling distributions and random variables are investigated. The solution is detailed and well presented.

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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