The length of time a traffic signal stays green (nicknamed the ʺgreen timeʺ)at a particular intersection follows a normal probability distribution with a mean of 200 seconds and the standard
Deviation of 10 seconds. Use this information to answer the following questions. Which of the
Following describes the derivation of the sampling distribution of the sample mean?
A)The standard deviations of a large number of samples of size n randomly selected from the population of ʺgreen timesʺ are calculated and their probabilities are plotted.
B)The mean and median of a large randomly selected sample of ʺgreen timesʺ are calculated. Depending on whether or not the population of ʺgreen timesʺ is normally distributed, either
The mean or the median is chosen as the best measurement of center.
C)The means of a large number of samples of size n randomly selected from the population of ʺgreen timesʺ are calculated and their probabilities are plotted.
D)A single sample of sufficiently large size is randomly selected from the population of ʺgreen timesʺ and its probability is determined.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean is derived by calculating the means of a large number of samples of size n randomly selected from the population and plotting their probabilities. This describes how the central limit theorem works, which states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

The Length of Time a Traffic Signal Stays Green (Nicknamed