u = 16 (the average number of orca calves in a pod each year)
o = 12 (the standard deviation)
n = 40 (the sample size)
u-x = u (mean of the sampling distribution = mean of the population) = 16
o-x = σ/√n = 12/√40 = 1.9 (standard deviation of the sampling distribution)
Here's the breakdown of each variable:
u: The population mean (µ) represents the average number of calves in an orca pod worldwide. In this case, µ = 16 calves.
o: The population standard deviation (σ) represents the variability in the number of calves across orca pods. In this case, σ = 12 calves.
n: The sample size (n) is the number of orca pods included in the study. In this case, n = 40 pods.
u-×: The sampling mean (µ-bar) represents the average number of calves in the sample of 40 pods. According to the Central Limit Theorem, µ-bar is approximately equal to µ, which is 16 calves.
o-×: The standard error of the mean (σ-bar) represents the variability in the sampling mean (µ-bar). It is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). In this case, σ-bar = σ/√n = 12 calves / √40 = 1.9 calves (rounded to the nearest whole number).
Question
Biologists are studying the distribution of the number of orca calves in pods worldwide. The average orca pod has 16 calves each year, with a standard deviation of 12 calves. Suppose a random sample of 40 pods is selected. Identify each of the following and make sure to round to the nearest whole number:
u=
o=
n=
u-×=
o-×=