Final answer:
To determine if a sample data set comes from a normally distributed population, you would use a normal quantile plot. Data points that closely align with a straight line suggest a normal distribution, while substantial deviation may indicate non-normality. The central limit theorem supports the normality of sample means for large sample sizes.
Step-by-step explanation:
In examining a normal quantile plot, we are looking to determine if the sample data could have come from a population with a normal distribution. A normal quantile plot, sometimes known as a Q-Q plot, is a graphical tool used to assess whether a set of data follows a normal distribution.
The data are plotted against a theoretical normal distribution in such a way that if the data are normally distributed, the points will fall approximately along a straight line. Any significant deviations from this straight line might indicate that the data are not normally distributed.
A normal distribution is a continuous distribution that is symmetric and bell-shaped, and it is very important in many fields such as psychology, business, and mathematics.
Its importance can be seen in various applications, where, for example, instructors may use it to determine grades, or it could be a good fit for variables like IQ scores and real-estate prices. However, it's crucial to understand that not all datasets will follow a normal distribution.
The central limit theorem and related rules tell us that, for a sufficiently large sample size (usually n > 30), the distribution of sample means will tend to be normal, regardless of the population's distribution.
This property is essential in statistics, as it allows for the use of normal distribution approximations for inferential statistics.