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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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
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Normal Distribution Quiz15 questions
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What is the probability that a continuous random variable takes definite value ?1 m
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For which value of standard normal variable, the standard normal curve is symmetric on both the sides?1 m
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Which value of normal variable divides the area of normal curve in two equal parts?1 m
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What percentage of area is covered under the normal curve within the range μ - 2σ to μ + 2σ ?1 m
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Mean of a normal distribution is 13.25 and its standard deviation is 10. Estimate the value of its third quartile.1 m
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For a normal distribution having mean 10 and standard deviation 6, estimate the value of quartile deviation.1 m
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The approximate value of mean deviation for a normal distribution 8. Find its standard deviation.1 m
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For a normal distribution, the estimated value of quartile deviation is 12. Find the value of its standard deviation.1 m
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For a probability distribution of standard normal variable, state the estimated limits for the middle 50 % observations.1 m
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The extreme quartiles of normal distribution are 20 and 30. Find its mean.1 m
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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
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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
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Chapter 3 Practice Material260 KB
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Statistics Important Theory2.9 MB
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