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The document covers various statistical concepts including Bayes' Theorem, Binomial and Normal Distributions, Hypothesis Testing, Rank Correlation, Poisson and Exponential Distributions, T-Distribution, and Regression Analysis. It includes specific problems and calculations related to these topics, such as calculating probabilities, testing hypotheses, and finding regression equations. Each section provides a framework for understanding and applying statistical methods in real-world scenarios.

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geetesh mishra
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7 views1 page

B

The document covers various statistical concepts including Bayes' Theorem, Binomial and Normal Distributions, Hypothesis Testing, Rank Correlation, Poisson and Exponential Distributions, T-Distribution, and Regression Analysis. It includes specific problems and calculations related to these topics, such as calculating probabilities, testing hypotheses, and finding regression equations. Each section provides a framework for understanding and applying statistical methods in real-world scenarios.

Uploaded by

geetesh mishra
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

Bayes' Theorem
(a) Explain Bayes' Theorem in probability with its real-world applications. (4 marks)
(b) A factory has two machines, Machine A and Machine B, that produce 70% and 30% of the total output, respectively. 4%
of items from Machine A and 6% of items from Machine B are defective. If a randomly selected item is defective, what
is the probability that it was produced by Machine A? (6 marks)
2. Binomial Distribution
(a) A student has a 60% chance of passing each exam. If he takes 8 exams, what is the probability that he passes exactly 5
exams? (5 marks)
(b) A hospital receives an average of 3 patients per hour with a particular condition. What is the probability that in a given
hour, they receive at most 4 such patients? (5 marks)
3. Normal Distribution
(a) The time taken by employees to complete a task is normally distributed with a mean of 15minutes and a standard
deviation of 3 minutes. What is the probability that a randomly selected employee takes more than 18 minutes to complete
the task? (5 marks)
(b) The heights of 1000 students in a class are normally distributed with a mean of 165 cm and standard deviation of 8 cm.
What percentage of students have a height between 160 cm and 170 cm? (5 marks)
4. Hypothesis Testing
(a) A manufacturer claims that the average lifespan of his product is 10 years. A random sample of30 products gives a mean
lifespan of 9.5 years with a standard deviation of 1.2 years. At the 5% significance level, test whether the average lifespan
is significantly different from 10 years. (10 marks)
5. Rank Correlation
Calculate the Spearman's rank correlation coefficient for the following data:
| X (Marks in Mathematics) | Y (Marks in Physics) |
|--------------------------|----------------------|
| 85 | 75 |
| 60 | 70 |
| 45 | 50 |
| 75 | 80 | | 90
| 95 |
(10 marks)
PART-C
6. Poisson Distribution
A factory has an average of 2 defects per day. What is the probability that exactly 3 defects occur on a particular day? (5 marks)
7. Exponential Distribution
The lifetime of a battery is exponentially distributed with a mean of 5 years. What is the probability that a randomly selected battery
lasts less than 3 years? (5 marks)
8. T-Distribution
A sample of 25 students has a mean weight of 60 kg with a standard deviation of 8 kg. Test whether the average weight of the students
differs significantly from the national average of 62 kg at the 1% significance level. (10 marks)
9. Regression Analysis
The following data represents the relationship between the number of hours studied and marks obtained in an exam:
| Hours Studied (X) | Marks Obtained (Y) |
|-------------------|-------------------|
|1 | 45 |
|2 | 50 |
|3 | 60 |
|4 | 70 |
|5 | 75 |
(a) Find the equation of the regression line Y = aX + b. (6 marks)
(b) Estimate the marks obtained if a student studies for 6 hours. (4 marks)

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