No. 2 week5-week7 Student Full Name:___________________________________ . Student ID:__________________________________________ . CRN No:____________________________________________ . STATISTICS (STAT-101) Branch: _____________________________________________. Total Points True/False ____/6 MCQ ____/6 Short Answer ____/18 Total ____/30 Good Luck STATISTICS (STAT-101) Marks- 30 Answer all the Questions on the same question paper. Section-I State whether the following statements are True or False. (6 marks, 1 Mark Each) 1. T The Student t distribution is same for different sample sizes. 2. TThe distribution of sample will, as the sample size increases, approach a normal distribution. . 3. FFor any normal distribution, the mean, median, and mode will have the same value. Page 2 of 6 4. TThe Central Limit Theorem tells us that as the sample size n increases, the sampling distribution of the sample mean will approach a binomial distribution. 5. If the z - score of normal distribution is 2, the mean of the distribution is 30 and the standard deviation of normal distribution is 9 then the value of X for a normal distribution is 48 6. TThe time it takes a randomly selected student to complete an exam is discrete random variable Section-II Mark the right answer from following multiple choice questions: (Multiple Choice Questions) (6 marks, 1 Mark Each) 1. A police department reports that the probabilities that 0, 1, 2 and 3 burglaries will be reported in a given day are 0.45, 0.44, 0.09 and 0.02, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth. a. = 0.52 b. = 0.72 c. = 0.99 d. =0.98 2. A distribution of data that is the left half of its histogram is roughly a mirror image of its right half called: a. Skewed b. Symmetric c. Both a and b d. None of the above Page 3 of 6 3. Which of the following is not a property of a binomial experiment? a. The experiment consists of n identical trials. b. The trials are independent, that is, the outcome of one trial does not influence the outcome of another. c. The two outcomes, success (S) and failure (F) are equally likely to occur. d. The probability of a success on a single trial is equal to p, and p remains constant from trial to trial. 4. The following confidence interval is obtained for a population proportion p: [0.528 , 0.554]. The margin of error E is equal to a. 0.013 b. 0.026 c. 0.011 d. 0.014 5. The critical value a. 1.340 b. 1.700 c. 1.645 d. 1.750 z / 2 that corresponds to a 90% confidence level is 6. An industrial designer wants to determine the average amount of time it takes an adult to assemble an \"easy to assemble\" toy. A sample of 16 times yielded an average time of 19.92 minutes, with a sample standard deviation of 5.73 minutes. Assuming normality of assembly times, provide a 95% confidence interval for the mean assembly time. a. 19.92 2.81 b. 19.92 3.05 c. 19.92 3.04 d. 19.92 2.51 Filling the table below is mandatory! MCQ 1 2 3 4 5 6 Answers Page 4 of 6 Section -III (18 marks, 3 Mark Each) Answer the following Essay Type Questions 1. X follows a normal distribution with mean =2 and variance 2 = 9 and Z denotes the corresponding standard normal distribution. Find a) b) c) 2. Twelve percent of computer parts produced by a certain supplier are defective. What is the probability that a sample of 10 parts contains a. No defective ones (i.e. P(X=0)) b. More than 3 defective ones (i.e. P(X>3)) 3. Given that, there is a 0.8 probability that a randomly selected adult knows what Facebook is, use the binomial probability formula to find, when 3 adults are randomly selected: A. P(X=2), i.e., 2 adults who know what Facebook is B. P(X at least 1), i.e., at least 1 adult who knows what Facebook is C. P(X at most 2), i.e., At most1 adult who knows what Facebook is 4. Suppose that you have a sample of 121 values from a population with mean = 500 and with standard deviation = 88. What is the probability that the sample mean will be in the interval (490, 510)? 5. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3 minutes. After observing 100 workers assembling similar devices, the manager noticed that their average time was 16 minutes. Construct a 90% confidence interval for the mean assembly time. 6. The random variable X has the following probability distribution: X P(x) 0 0.2 1 0.1 Page 5 of 6 2 0.4 3 K a. Find K to Prove that the given table satisfied a probability distribution b. Find the mean & the Variance. Page 6 of 6