1) The probability distribution of a discrete random variable is also called _______________. a) Probability mass function b) Probability weight function c) Probability correspondence d) Probability Distribution of a Continuous Random variable 2) Which of the following is the value of it’s variance if the value of the standard deviation of the given probability distribution is 6? a) 6 b) 36 c) 72 d) 98 3) What happens to a normal distribution curve when the standard deviation increases? a) The curve becomes wider b) The curve becomes taller c) The curve becomes narrower d) The curve shifts to the right 4) What percentage of data lies between z = -1 and z = 1 in a standard normal distribution? a) 50% b) 68.27% c) 95.45% d) 99.73% 5) What sampling method involves listing population members and selecting samples at fixed intervals, known as sample intervals? a) Quota sampling b) Lottery sampling c) Systematic sampling d) Stratified random sampling 6) Which of the following most accurately explains the difference between a parameter and a statistic? a) A parameter and a statistic are essentially the same thing, just with different names depending on the context. b) Both a parameter and a statistic refer to numerical summaries of a sample, but a statistic is always more precise. c) A parameter is a numerical summary of a sample, while a statistic is a numerical summary of an entire population. d) A parameter is a numerical summary of an entire population, while a statistic is a numerical summary of a sample. 7) Which of the following is TRUE about the relationship between the population mean μ and the mean of the sampling distribution of the sample mean μ sub x̅ ? a) μ sub x̅ is always smaller than μ b) μ sub x̅ depends on the sample size n c) μ sub x̅ equals μ regardless of sample size d) μ sub x̅ equals μ only for normal populations 8) What formula is used to estimate population parameters when the variance is unknown? a) b) c) d) 9) How is the standard error of the sample mean determined when the population variance is known or unknown? a) b) c) d) 10) What does the Central Limit Theorem explain about the mean of the sampling distribution of the sample mean? a) The mean of the sampling distribution of the sample mean is larger than the population mean. b) The mean of the sampling distribution of the sample mean is exactly equal to the population mean. c) The mean of the sampling distribution of the sample mean is close to the population means if the sample size is large. d) The mean of the sampling distribution of the sample mean is equal to the population mean divided by the square root of the sample size. 11) What is the mean of the sampling distribution if the population mean is 19.5? a) less than 19.5 b) larger than 19.5 c) closer to 19.5 d) exactly the same as 19.5 12) What is the standard error of the mean when the sample size is 15 and the population standard deviation is 20? Use the formula S=σ/√n a) 5.16 b) 5.17 c) 5.18 d) 5.19 13) What is the mean and standard deviation of the sampling distribution of the mean when n = 14, given a population mean of 30 and a standard deviation of 5? a) X ̅=15,s=1.30 b) X ̅=15,s=1.34 c) X ̅=30,s=1.34 d) X ̅=30,s=1.30 14) What does the standard error of the mean represent? a) The variability of the individual data points in a dataset. b) The measure of the average deviation of individual data points from the mean. c) The degree of accuracy of the sample means as an estimate of the population mean. d) The average of the squared differences between the sample mean and the population mean. 15) What are all the possible samples of size 2 that can be drawn with replacement from a population containing the values {2, 4, 6}? a) {2,4,6} b) {(2,2),(2,4),(2,6),(6,2),(6,4),(6,6)} c) {(2,2),(2,4),(2,6),(4,2),(4,4),(4,6)} d) {(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)} 16) Which of the following cases is the sample size considered sufficiently large? a) n≥30 b) n≤30 c) n≥50 d) n≤50 17) Which probability distribution is used when the population variance is unknown and/or the sample size is small? a) chi distribution b) p-distribution c) t-distribution d) z-distribution 18) Who introduced the t-distribution in 1908? a) Ronald A. Fisher b) Wilhem G. Student c) William S. Gosset d) William A. Student 19) What is the probability that the student is wearing rubber shoes if a student is selected randomly in a class of 40 students, eight are wearing rubber shoes? a) 2/10 b) 3/10 c) 8/40 d) 40/40 20) Consider the discrete random variable Z with the following probability distribution: P(Z = 1) = 0.6, P(Z = 2) = 0.3, P(Z = 3) = 0.2, and P(Z = 5) = 0.1. What is the mean of Z? a) 2.1 b) 2.2 c) 2.3 d) 2.4 21) Given a discrete random variable N, with a mean of 5 and a variance of 1, which one of the following statements is true? a) N is always equal to 5 with no variation. b) N has a probability distribution that is heavily skewed. c) The values of N are concentrated around the mean with little spread. d) On average, N is expected to take values near 5, and the values of N are spread out by a factor of 1. 22) What is the probability of randomly selecting a value with a z-score greater than 2.33 in a standard normal distribution? a) 0.01 b) 0.05 c) 0.25 d) 0.001 23) Using the standard normal table, what is the z-score corresponding to the 90th percentile? a) 0.90 b) 1.28 c) 1.96 d) 1.645 24) A college aims to estimate the average weekly study time of its students. With a total of 5,000 students, a researcher randomly selects a sample of 50 students, records their weekly study hours, and calculates the sample mean. Which of the following statements correctly describes the sampling distribution of the sample mean? a) It is a distribution of the weekly study hours for all 5,000 students. b) It is a single value representing the mean study hours of the sample. c) It is the difference between the largest and smallest study hours in the sample. d) It is a distribution of the sample means calculated from repeated samples of 50 students each, taken from the population. 25) A bakery's daily cupcake sales are normally distributed with a mean of 120 cupcakes and a standard deviation of 15 cupcakes. If the bakery randomly selects samples of 25 days and calculates the sample mean for each sample, what is the variance of the sampling distribution of these sample means? a) b) c) d) 26) What is the implication of the t-distribution having thicker tails than the normal distribution? a) The normal distribution has a greater mean than the t-distribution. b) The t-distribution has lesser variability than the normal distribution. c) The t-distribution has a greater chance for extreme values than the normal distribution. d) Estimation of the parameter using the z-distribution is more accurate than using the t-distribution. 27) Given that both teams have an average score of 60, with team A having a variance of 16 and team B having a variance of 9, how can you determine which team is more consistent, and in what ways could this information be applied? a) Both teams are equally consistent, as they have the same mean score. b) Team A is more consistent because their mean score is the same as Team B’s. c) Team B is more consistent because their variance is smaller, indicating less fluctuation in their performance. d) Team A is more consistent because they have a larger variance, indicating higher reliability in performance. 28) A discrete random variable D denotes the number of defective items identified in a sample of 5 items. The probability distribution is given as follows: "What is the variance of D?" a) 0.8 b) 1.0 c) 1.5 d) 0.6 29) What is the probability notation for the scenario where the mean time the group takes to complete the test is between 49.5 and 54 minutes? a) P(49.5<X ̅<54) b) P(49.5>X ̅>54) c) P(54<X ̅<49.5) d) P(54<X ̅>49.5) 30) What are the standard scores if we convert the observed value? a) z_1=-1.98,z_2=1.20 b) z_1=1.98,z_2=-1.20 c) z_1=-2.98,z_2=2.20 d) z_1=2.98,z_2=-2.20

STATISTICS AND PROBABILITY

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