Basic Statistics 2079

Section A

Long Answer Questions
Attempt any TWO questions. [2 × 10 = 20]

1. What is the difference between relative and absolute statistical measures? J.J. Thomson discovered the electron by isolating negatively charged particles for which he could measure the mass-charge ratio. This ratio appeared to be constant over a wide range of experimental conditions and, consequently, could be characteristic of new particles. His observations from two different Cathode-ray tubes that used air as the gas are:

2. In Nepal, during the fall harvest season, pumpkins are sold in large quantities at farm stands. Often, instead of weighing the pumpkins prior to sale, the farm stand operators place the pumpkins in the appropriate circular cutout on the counter. When asked why this was done, one farmer replied, 'I can tell the weight of the pumpkin from its circumference.' To determine whether this was really true, a sample of 8 pumpkins' circumferences and weights were measured:

3. Define normal distribution and standard normal distribution. In an examination, 10% of students got less than 20 marks and 95% got less than 75 marks. Assuming the distribution to be normal, find the mean and standard deviation. [10]

Section B

Short Answer Questions
Attempt any EIGHT questions. [8 × 5 = 40]

4. What do you mean by secondary data? Write the sources of secondary data with a special focus on the Nepalese context. [5]

5. Construct a histogram, frequency polygon, and frequency curve of the following frequency distribution:

6. The following data represent the preference of 10 students studying BIT towards two brands of computers, namely DELL and HP:

7. Define random variable. A random variable has the following probability function:

8. During one stage in the manufacture of integrated circuit chips, a coating must be applied. If 70% of chips receive a thick enough coating, find the probability that among 15 chips (i) at least 12 will have thick enough coatings, (ii) at most 2 will have thick enough coatings, and (iii) exactly 10 will have thick enough coatings. [5]

9. A new computer virus can enter the system through e-mail or through the internet. There is a 30% chance of receiving this virus through e-mail. There is a 40% chance of receiving it through the internet. Also, the virus enters the system simultaneously through e-mail and the internet with a probability of 0.15. What is the probability that the virus does not enter the system at all? [5]

10. The standard deviation of a symmetric distribution is 9. Compute the possible value of the fourth central moment for the distribution to be (i) mesokurtic, (ii) platykurtic, and (iii) leptokurtic. [5]

11. The mass of vitamin E in a capsule manufactured by a certain drug company is normally distributed with a standard deviation of 0.042 mg. A random sample of 36 capsules was analyzed, and the mean mass of vitamin E was found to be 5.12 mg. Calculate a symmetric 95% confidence interval for the population mean mass of vitamin E per capsule. [5]

12. Write short notes on the following:

• a. Box and whisker plot
• b. Census survey and sample survey