MCom I Semester Statistical Analysis Theoretical Frequency Distribution Study Material notes ( part 3)

MCom I Semester Statistical Analysis Theoretical Frequency Distribution Study Material notes ( part 3) : Equation of the Normal Curve Fitting of Normal Curve Heights of Ordinates at Various Mid Values Important Formular of Theoretical Frequency Distribution at a Glace Examinations Questions Long Answer Questions Short Answer Questions Objectives Questions

MCom I Semester Business Environment GSTP GSP Counter Trade Study Material Notes

 Theoretical Frequency Distribution Study Material notes ( part 3)

Illustration 32.

of a large group of men, 5% are under 60 inches in height and 40% are between 60 and 65 inches. Assuming a normal population, find the mean height and standard deviation. Solution.

Let the random variable X represent the height of men and X and o be mean and standard deviation respectively of the normal distribution.

Since height of 5% men are under 60 inches, it means probability (X < 60) = 0.05 and height of 40% men are between 60 and 65 inches it means probability (60 < X < 65) = 0.40. .. % of men under 65 inches would be = 5 + 40 = 45 i.e., probability

(X < 65) = 0.45 Since the total area to the left of the ordinate at X = 0.5, both the points X = 60 and X = 65 are located to the left of X and consequently the corresponding values of z are negative. We obtain the following value of z from normal curve table :

Standard Normal Variety (2) for area of 0.4500 = 1.645 and Standard Normal Variety (z) for area of 0.0500 = 0.13 (approx.) On the basis of above information, we obtain the following two equations :

EXAMINATION QUESTIONS

Long Answer Theoretical Questions

1 What is meant by theoretical frequency distributions? Discuss the salient features of the Normal and Poisson Distributions.

2. Distinguish between the normal and binomial distributions and discuss briefly the importance of normal distribution for statistical inference.

3. How does a normal distribution differ from a binomial distribution ? Mention the properties of a normal distribution. How are they useful in random sampling investigation ?

4. Give the chief characteristics of the normal distribution. Under what circumstances does the binomial tend to the normal distribution

5. List the chief properties of normal distribution. Why is this distribution given a central place in statistics ?

6. What is meant by ‘Theoretical Frequency Distribution’? Discuss the saline features of Binomial, Normal and Poisson Distribution.

7. State and compare the distinctive features of the Binomial, Poisson and Normal probability distributions. When does a Binomial distribution tend to become a Normal and a Poisson distribution ?

Short Answer Theoretical Questions

1 Give the main characteristics of Normal Distribution.

2. Explain the characteristics of Poisson Distribution.

3. State the general rules of writing Binomial distribution.

4. Name the six situation where Poisson distribution can have applications.

5. How are the values of mean and standard deviation calculated in Binomial and Poisson distributions ?

6. Define Binomial Distribution.

7. Explain the characteristics of Binomial Distribution.

8. What is meant by ‘Theoretical Frequency Distribution’?

9. When does a binomial distribution tends to become a Normal and Poisson distribution ?

10. How does a Normal Distribution differ from a Binomial Distribution ?

Objective Questions the following statements are ‘True’ or ‘False :

1 A normal curve is completely defined by mean and the standard deviation.

2. (p+q) = p + 5p+q’ + 10pq? + 10p-q3 + 5p’94 +95

(True)

3. The mean and variance of a Poisson distribution are equal.

(True)

4. The normal distribution is completely determined if the value of u and o- are

known.

5. In a Poisson Distribution as N increases, the distribution shifts to the right.

(True)

6. In a Binomial Distribution, the mean and the variance are the same. (False)

(True)

7. Binomial Probability Distribution is a distribution for dealing with quantities whose magnitude vary continuously.

(True)

8. The mean of binomial distribution is vnp and its standard deviation is npq.

(False)

9. The normal distribution was first discovered by De Moiré in 1773. (True)

10. In a binomial distribution B. = (q + p)2/npq.

(False)