Chapter 3: Normal Distribution

Normal Distribution is the father of all probability distributions. For larger sample size almost all theoretical distributions follow it.

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Details

In this course, we inspect the probability distribution for a continuous random variable.
We know that, if a random variable X can assume any value of real set R or within any interval of real set R, then it is called a continuous random variable. If a random variable can assume any value between the definite interval a to b, then it is denoted by a < x < b.

A function for obtaining probability that a continuous random variable assumes value between specified interval is called the probability density function of that variable and it satisfies the following two conditions:

1. The probability that the value of random variable lies within the specified interval is non-negative.
2. The total probability that the random variable assumes any value within the specified interval is one.

Normal distribution is a very important probability distribution among probability distributions for continuous random variable and is very useful for higher statistical study.

Curriculum

Basic Concepts
  • Lecture 1
    34 m 37 s

Sums to Find Probability
  • Lecture 2
    35 m 55 s

Sums to Find Z
  • Lecture 3
    27 m 22 s

Important Sums
  • Lecture 5
    25 m 33 s
  • Lecture 6
    27 m 10 s
  • Lecture 7
    52 m 7 s
  • lecture 8
    51 m 13 s
  • Lecture 9
    47 m 7 s

Objectives
  • Normal Distribution Quiz
    15 questions
  • What is the probability that a continuous random variable takes definite value ?
    1 m
  • For which value of standard normal variable, the standard normal curve is symmetric on both the sides?
    1 m
  • Which value of normal variable divides the area of normal curve in two equal parts?
    1 m
  • What percentage of area is covered under the normal curve within the range μ - 2σ to μ + 2σ ?
    1 m
  • Mean of a normal distribution is 13.25 and its standard deviation is 10. Estimate the value of its third quartile.
    1 m
  • For a normal distribution having mean 10 and standard deviation 6, estimate the value of quartile deviation.
    1 m
  • The approximate value of mean deviation for a normal distribution 8. Find its standard deviation.
    1 m
  • For a normal distribution, the estimated value of quartile deviation is 12. Find the value of its standard deviation.
    1 m
  • For a probability distribution of standard normal variable, state the estimated limits for the middle 50 % observations.
    1 m
  • The extreme quartiles of normal distribution are 20 and 30. Find its mean.
    1 m
  • The age of a group of persons follows normal distribution with mean 45 years and standard deviation 10 years. Calculate Z-score for a randomly selected person having age 60 years.
    1 m
  • The age of a group of persons follows normal distribution with mean 45 years and standard deviation 10 years. Calculate Z-score for a randomly selected person having age 60 years.
    1 m
  • Chapter 3 Practice Material
    260 KB
  • Statistics Important Theory
    2.9 MB
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  • 1 quiz
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