NO. 2 Student Full Name:___________________________________ . Student ID:__________________________________________ . CRN No:____________________________________________ . Branch: _____________________________________________. STATISTICS (STAT-101) Total Points True/False ____/5 MCQ ____/5 Short Answer ____/15 Total ____/25 Good Luck STATISTICS (STAT-101) Marks- 25 Answer all the Questions on the same question paper. Section-I State whether the following statements are True or False. (5 marks, 1 Mark Each) 1. Mean value over an infinite number of observations of the variables is the expected value of random variables. 2. A standard normal distribution has the mean equal to the variance. 3. A sampling distribution of the mean has mean of and standard deviation of . 4. A critical value is a z score separating unlikely values from those that are likely to occur. 5. It is 90% (or 0.90) confidence level for corresponding value of = 0.20 Section-II (Multiple Choice Questions) (5 marks, 1 Mark Each) 1. Which one of these variables is a continuous random variable? a) The time it take a randomly selected student to complete an exam b) The number of children in a family c) The number of women taller than 68 inches in a random sample of 5 women. d) The number of correct guesses in a multiple-choice test. Page 2 of 4 2. A compagny manufactures batteries in batches of 13 and there is a 3% rate of defects. Find the mean number of defects per batch. a) b) c) d) 0.4 12.6 0.39 39 3. If the z - score of normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation of normal distribution is 3 then the value of X for a normal distribution is a) b) c) d) 97.5 47.5 52.5 67.5 4. If the sampling error (E) is allowed to increase, which of the following is true regarding the sample size? a) b) c) d) The sample size will increase The sample size will decrease The sample size will stay the same The sample size cannot be determined 5. Use the confidence level and sample data to find a confidence interval for estimating the population . Round your answer to the same number of decimal places as the sample mean. Given: n = 105; x = 70.5; = 6.8; 99% confidence. a) b) c) d) 9.0 < < 72.0 68.8 < < 72.2 69.2 < < 71.8 None. Part-II (Multiple Choice Questions) MCQ 1 2 3 4 5 Answers Page 3 of 4 (5 marks, 1 Mark Each) Section -III Answer the following Essay Type Questions (15 marks, 5 Mark Each 1. During the summer months, a rental agency keeps track of the number of chain saws it rents each day during a given period and X denotes the number of saws rented per day: a) Check a probability distribution. b) Find the mean, variance, and standard deviation for the probability distribution. X 0 1 2 P(x) 0.6 0.33 0.07 2. If X is binomially distributed with 5 trials and a probability of success equal to 0.3 at each attempt. a) What is the probability of exactly 4 successes? b) Also find the parameter mean, variance and standard deviation? 3. Find a) P (z < 2.37) b) P (z > 1.82) c) P (-1.18 < z < 2.1) Good luck Page 4 of 4