Final answer:
The normal distribution is a continuous probability distribution that is symmetrical around its mean. To form debate teams of three from twelve students, 220 different teams can be formed using combinations. The binomial distribution is a discrete distribution and may be approximated by the normal distribution under certain conditions.
Step-by-step explanation:
The normal distribution is characterized by certain features that distinguish it from other types of distributions.
Normal Distribution Characteristics
It is a continuous probability distribution, meaning that it allows for an infinite number of possible outcomes within a given range.
The normal distribution is symmetrical around its mean.
In a graph of a normal distribution, the majority of the data falls within a small range of values, with the probability of extreme values tapering off symmetrically on both sides.
Formation of Debate Teams
To calculate how many different debate teams of three members can be formed from a pool of twelve students, we use the combination formula:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items, and k is the number of items to choose.
Here, n = 12 and k = 3.
C(12, 3) = 12! / (3!(12-3)!) = (12×11×10) / (3×2×1) = 220 different teams.
Continuous vs Discrete Data
Discrete data refers to data points that are distinct and separate, typically counted in whole numbers.
Continuous data involves measurements and can take on any value within a given range.
Comparison Between Binomial and Normal Distribution
The binomial distribution is a discrete probability distribution, describing the outcome of n independent trials in an experiment. The normal distribution is often used as an approximation to the binomial distribution when n is large, and the probability of success p is not too close to 0 or 1.
Quantitative Continuous Data
Quantitative continuous data consists of numerical measurements that can take on any value within a continuous range.