IY2 Quantitative Methods for Computing Past Paper PDF

## IY2 Quantitative Methods for Computing **Duration: 60 minutes** Please choose the most appropriate answer from the options given. 1. A company recorded the ages of five employees: 22, 18, 20, 25, and 15. After arranging the data in ascending order, calculate the Interquartile Range (IQR) by fi...

## IY2 Quantitative Methods for Computing **Duration: 60 minutes** Please choose the most appropriate answer from the options given. 1. A company recorded the ages of five employees: 22, 18, 20, 25, and 15. After arranging the data in ascending order, calculate the Interquartile Range (IQR) by first finding the lower quartile (Q1), the upper quartile (Q3), and then subtracting Q1 from Q3. * a) 7 * b) 6 * c) 8 * d) 9 2. You have a deck of 52 cards. What is the probability of drawing a spade, followed by a diamond, followed by a heart, without replacement? What is the probability of getting a Spade, Diamond and Heart. * a) 1/52 * b) 1/204 * c) 13/2652 * d) 12/2652 3. If you take repeated samples of size 30 from a population with a mean of 55 and a standard deviation of 15. What is the Standard Error of the Mean? * a) 1.5 * b) 2.7 * c) 3 * d) 2 4. A survey was conducted on 160 students to determine their preferred method of transportation to school. The results were recorded as follows: | Transportation Method | Number of Students | |---|---| | Car | 70 | | Bus | 50 | | Bicycle | 30 | | Walking | 5 | | Other | 5 | What is the probability that a randomly selected student prefers either Car or Bus as their mode of transportation? * a) 0.69 * b) 0.61 * c) 0.75 * d) 0.50 5. Which of the following statements is true regarding the relationship between the population, sample distribution, and confidence intervals? * a) A confidence interval can be constructed using the population mean and standard deviation, regardless of the sample size. * b) The sampling distribution of the sample mean becomes approximately normal when the sample size is large enough, regardless of the population distribution. * c) The population standard deviation must always be known to construct a confidence interval for the population mean. * d) A confidence interval provides an exact value for the population mean, with no margin of error. 6. In a batch of 12 batteries, 4 are faulty. If two batteries are selected randomly without replacement, what is the probability that both batteries are faulty? * a) 1/15 * b) 1/30 * c) 1/11 * d) 4/66 7. Consider a discrete random variable X with the following probability distribution: | X | P(X=x) | |---|---| | 1 | 0.1 | | 2 | 0.2 | | 3 | 0.3 | | 4 | 0.4 | What is the expected value E(X) and variance Var(X) of the random variable X? * a) E(X)=3.0, Var(X)=1.0 * b) E(X)=2.5, Var(X)=0.5 * c) E(X)=2.5, Var(X)=1.0 * d) E(X)=3.0, Var(X)=0.5 8. The dataset consists of the following information about the heights of 12 individuals (in centimeters): 147.5, 154.3, 165.8, 157.1, 174.6, 182.3, 160.2, 169.9, 178.4, 164.0, 146.5, 152.5 Which of the following statements is true about this data? * a) It is continuous numerical data because it can take any value within a range. * b) It is discrete numerical data because it involves a countable set of possible values. * c) It is ordinal data because the heights can be ranked. * d) It is categorical data because it represents a group of individuals. 9. Out of 120 survey participants, 70 prefer tea, 50 prefer coffee, and 30 like both. If a participant is known to prefer tea, what is the probability that they also prefer coffee? * a) 3/7 * b) 2/5 * c) 1/4 * d) 1/6 10. A test score follows a normal distribution with a mean of 70 and a standard deviation of 10. What is the probability that a randomly selected test score is greater than 85? * a) 0.8413 * b) 0.1587 * c) 0.0228 * d) 0.9772 11. Two cards are drawn sequentially without replacement from a standard deck of 52 cards. What is the probability that the second card is a king, given that the first card drawn is a jack? * a) 1/13 * b) 4/51 * c) 3/51 * d) 1/52 12. Which of the following statements best describes sampling error in the context of statistical inference? * a) Sampling error occurs when the sample mean is exactly equal to the population mean. * b) Sampling error is the difference between a sample statistic and the corresponding population parameter, which can arise due to random variability. * c) Sampling error is always the result of bias in the data collection process. * d) Sampling error refers to the systematic deviation between the sample data and the population data, regardless of the sample size. 13. A population has a standard deviation of 20, and a sample of size 64 is taken from this population. What is the standard error of the mean (SEM) for the sample mean? * a) 2.5 * b) 5 * c) 10 * d) 20 14. The weight (in kilograms) of a randomly selected adult male follows a normal distribution with a mean of 70 kg and a standard deviation of 12 kg. What is the probability that a randomly selected male weighs more than 85 kg? * a) 0.1587 * b) 0.0228 * c) 0.8413 * d) 0.9772 15. If you have collected a random sample of 45 data points from a population with an unknown mean and variance. The sample has a mean of 15 and a variance of 5. If you were to take another random sample of 45 data points from the same population, which of the following statements is most likely true? * a) The sample mean will always be 15, and the sample variance will always be 5. * b) The sample mean will be close to 15, and the sample variance will be close to 5, but exact values may differ. * c) The sample mean will be 13, and the sample variance will be 2.5. * d) he sample mean and variance could be any values, not related to 15 and 5 at all. 16. Which of the following factors does not directly affect the width of a confidence interval for the population mean? * a) Sample size * b) Population standard deviation * c) Confidence level * d) Sample mean 17. Two dice are rolled, and the sum of the numbers on the dice is noted. What is the probability that the sum is 7 and at least one die shows a 3? * a) 1/18 * b) 2/36 * c) 1/9 * d) 2/12 18. Which of the following statements accurately describes the relationship between the sample mean and the population mean in the context of statistical estimation? * a) The sample mean is an unbiased estimator of the population mean, meaning that the expected value of the sample mean equals the population mean. * b) The sample mean always equals the population mean when the sample size is sufficiently large. * c) The sample mean systematically overestimates the population mean as the sample size increases. * d) The sample mean is always higher than the population mean, regardless of the sample size. 19. A researcher has conducted a study and calculated a sample mean of 50 with a standard deviation of 10. The sample size is 100. What is the 95% confidence interval for the population mean? * a) (48.0, 52.0) * b) (49.5, 50.5) * c) (47.0, 53.0) * d) (45.0, 55.0) 20. Which of the following statements is true about the standard error of the mean? * a) It is always smaller than the population standard deviation. * b) It increases with the sample size. * c) It is unaffected by the sample size. * d) It is calculated by dividing the sample standard deviation by the square root of the sample size.