Chapter 3: Normal Distribution

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

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

  • Lecture 1
    34 m 37 s
  • Lecture 2
    35 m 55 s
  • Lecture 3
    27 m 22 s
  • 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
  • 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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