Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Normal Distribution: Characteristics and Z-scores

In course

MICRO-110: Probability & statistics for engineers

Description

This lecture covers the characteristics of the normal distribution, including examples of dice throwing and the calculation of areas under the curve. It also explains Z-scores and their significance in normalizing populations. Additionally, it delves into the importance of probability in inferential statistics, illustrating how it links samples to populations and aids in making general conclusions. The lecture further explores how to check if an experimental factor affects a measured response, the effect of sample size on distribution, and the concept of repeated sampling from a population. Lastly, it discusses the binomial distribution and its approximation to a normal distribution under certain conditions.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Vivek Subramanian

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Sample size determination

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

Stratified sampling

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population.

Related lectures (36)

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

Probability and Statistics

Covers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Normal Distribution: Properties and Calculations