RGUHS Pharma D Important Questions (Question Bank)
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DEPARTMENT OF MATHEMATICS
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QUESTION BANK
I SEMESTER
1918108 - STATISTICS FOR MANAGEMENT
Regulation – 2019
Academic Year 2019 - 2020
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Prepared by
Ms. B. Vasuki, Assistant Professor/Mathematics
Ms.B.Elakkiavani, Assistant Professor/Mathematics
SUBJECT : 1918108 – STATISTICS FOR MANAGEMENT
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SEM / YEAR : I Semester / I Year
UNIT I - INTRODUCTION
SYLLABUS: Basic definitions and rules for probability, conditional probability independence of events, Baye's theorem, and random variables, Probability distributions: Binomial, Poisson, Uniform and Normal distributions.
PART- A
| S.NO | QUESTIONS | BT Level | COMPETENCE |
|---|---|---|---|
| PART - A | |||
| 1. | Define Statistics. | BTL-6 | Creating |
| 2. | What is the addition and multiplication theorem on probability. | BTL -1 | Remembering |
| 3. | Distinguish between a priori and posterior probability?. | BTL-6 | Creating |
| 4. | The price of the selected stock over a five day period shown as 170, 110, 130, 170 and 160. Compute mean, median and mode. | BTL-6 | Creating |
| 5. | A car travels 25 miles at 25 mph, 25 miles at 50 mph and 25 miles at 75 mph. Find the harmonic of three velocities? | BTL-4 | Analyse |
| 6. | A ball is drawn at random from a box containg 6 red balls, 4 white balls and 5 blue balls. Find the probability that the ball drawn is not red. | BTL-4 | Analyse |
| 7. | Find the median and mode for the weights (kgs) of 15 persons given as 68, 85, 70, 65, 71, 67, 65, 55, 80, 62, 65, 64, 70, 60, 56. | BTL-3 | Applying |
| 8. | Name few measures of dispersion. | BTL-1 | Remembering |
| 9. | write the common measures of central tendency? | BTL-1 | Remembering |
| 10. | Define continuous and discrete variables examples. | BTL-1 | Remembering |
| 11. | Let X be the lifetime in years of a mechanical part. Assume that X has the cdf F(x) = 1- e-x, x > 0. Find P[1< X <3]. | BTL-1 | Remembering |
| 12. | Define independent events. | BTL-1 | Remembering |
| 13. | State the theorem of total probability | BTL-1 | Remembering |
| 14. | What is the use of Baye's theorem? | BTL-6 | Creating |
| 15. | Mention the properties of a discrete probability distribution. | BTL-1 | Remembering |
| 16. | Define a Poisson distribution and mention its mean and variance. | BTL-1 | Remembering |
| 17. | If the mean and variance of a binomial distribution are respectively 6 | BTL -3 | Applying |
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| 18. | and 2.4, find P(x=2). If x is a Poisson distribution such that P(x=1)=4P(x=2). Find its mean and variance. | BTL-3 | Applying |
| 19. | Suppose that X has a Poisson distribution with parameter ? = 2. Compute P[X > 1]. | BTL-1 | Remembering |
| 20. | Define mutually exclusive events. | BTL-1 | Remembering |
PART-B
| 1(a). | Calculate the mean and standard deviation for the following table giving the age distribution of 542 members.
| BTL-2 | Understanding | ||||||||||||||||||||||||||||
| 1(b). | Find the geometric mean for the following data:
| BTL-2 | Understanding | ||||||||||||||||||||||||||||
| 2(a). | Find the mean, median and modal ages of married women at first child birth
| BTL-6 | Creating | ||||||||||||||||||||||||||||
| 2(b). | If A and B are independent event with P(A)=2/5, and P(B)=3/5, find P(AUB). Let S= {1,2,3,4,5,6} if A = {2,4,6} then find the probability of A complement. | BTL-3 | Applying | ||||||||||||||||||||||||||||
| 3(a). | Given: The probabilities of three events A, B and C occurring are P(A) = 0.35, P(B) = 0.45 and P(C) = 0.2. Assuming that A, B, or C has occurred, the probabilities of another event X occurring are P(X/A) = 0.8, P(X/B) = 0.65 and P(X/C) = 0.3. Find P(A/X), P(B/X) and P(C/X). | BTL-6 | Creating | ||||||||||||||||||||||||||||
| 3(b). | 4 cards are drawn from a well shuffled pack of cards. Find the probability that (i) All the four are queens (ii) There is one card from each suit. (iii) Two cards are diamonds and two are spades All the four cards are hearts and one of them is jack | BTL-6 | Creating | ||||||||||||||||||||||||||||
| 4(a). | Three machines all turn out non ferrous castings. Machine A produces 1% defective and Machine B- 2% and machine C – 5%. Each machine produces 1/3 of the output. An inspector examines a single casting, which he determines as non defective. Estimate the probabilities of its having been produced by each machine. | BTL -6 | Creating | ||||||||||||||||||||||||||||
| 4(b). | If the random variable X takes values 1, 2, 3, 4 such that 2P(X = 1) = 3P(X = 2) = P( X=3) = 5P(X = 4), find the probability distribution and cumulative distribution of X. | BTL-2 | Understanding | ||||||||||||||||||||||||||||
| 5(a). | Two dice are thrown together once. Find the probabilities for | BTL -3 | Applying |
| 5(b). | getting the sum of the two numbers (i) equal to 5, (ii) multiple of 3, (iii) divisible by 4. Given ? = 4.2, for a poisson distribution. Find (a) P(X = 2) (b) P(X = 5) (c) P(X = 8). | BTL-6 | Creating |
| 6(a). | An urn contains 5 balls. Two balls are drawn and found to be white. What is the probability that all the balls are white? | BTL-1 | Remembering |
| 6(b). | The contents of urns I, II, III are as follows: 1 white, 2 black and 3 red balls; 2 white, 1 black and 1 red balls; 4 white, 5 black and 3 red balls; One urn is chosen at random and two balls drawn. They happen to be white and red. What is the probability that they come from urns I, II, III? | BTL-3 | Applying |
| 7(a). | In 1989, there were three candidates for the position of principal Mr. Chatterji, Mr. Ayangar and Dr. Singh. Whose chances of getting the appointment are in the proportion 4:2:3 respectively. The probability that Mr. Chatterji is selected, would introduce co- education in the is 0.3. The probabilities of Mr. Ayangar and Dr. Singh doing the same are respectively 0.5 and .08. What is the probability that there was co-education in the in 1990? | BTL-3 | Applying |
| 7(b). | Find the probability that atmost 5 defective bolts will be found in a box of 200 bolts, if it is known that 2% of such bolts are expected to be defective. (e-2= 0.0183) | BTL-6 | Creating |
| 8(a). | A coin is tossed 6 times what is the probability of obtaining (a) 4 heads (b) 5 heads (c) 6 heads (d) getting 4 or more heads. | BTL-3 | Applying |
| 8(b). | In a bolt factory machines A, B, C manufacture respectively 25%, 35% and 40% of the total of their output 5, 4, 2 percent are defective bolts. If A bolt is drawn at random from the product and is found to be defective, what are the probabilities that is was manufactured by machines A, B and C? | BTL-6 | Creating |
| 9(a). | In a test of 2000 electric blubs it was found that the life of a particular make was normally distributed with an average life of 2040 hours and S. D. of 60 hours. Estimate the number of blubs likely to burn for (1) More than 2150 hours (2) Less than 1950 hours (3) More than 1920 hours but less than 2160 hours. | BTL-3 | Applying |
| 9(b). | The latest nationwide political poll indicates that for Americans who are randomly selected, the probability that they are conservative is 0.55, the probability that they are liberal is 0.30 and the probability that they are middle of the road is 0.15. Assuming these probabilities are accurate, answer the following | BTL -4 | Analyzing |
| 10. | questions from a randomly chosen group of 10 Americans (a) What the probability that 4 are liberal? (b) What the probability that none are conservative (c) What the probability that two are middle of the road (d) What the probability that a least 8 are liberal If X follows a normal distribution with mean 12 and variance 16 cm, find the probabilities for (i) X = 20 (ii) X > 20, and (iii) 0 = X 12. | BTL -3 | Applying | ||||||||||||||||||||
| 11. | A discerete random variable X has the probability function given below: Value of X=x: 0 1 2 3 4 5 6 7 P(X=x) : 0k 2k 2k 3k k² 2k² 7k²+k Find (1) The value of k (2) P(1.5 < X < 4.5 / X > 2) (3) P(X < 6), P(X = 5), P( 0 < X <4) (4) The distribution of X. | BTL-3 | Applying | ||||||||||||||||||||
| 12. | X is a normal variable with mean 30 and standard deviation of 5. Find (i) P[26 = X = 40] (ii) P [X=45] (iii) P [ |X - 30|> 5] use normal distribution tables | BTL-4 | Analyzing | ||||||||||||||||||||
| 13. | In an intelligence test administered on 1000 students, the average was 42 and standard deviation 24, find (i) the number of students exceeding a score 50. (ii) the number of students lying between 30 and 54(iii) the value of score exceeded by top 100 students. | BTL-4 | Analyzing | ||||||||||||||||||||
| 14(a). | The probability that an entering student will graduate is 0.4 Determine the probability that out of 5 students atleast one will graduate. | BTL-5 | Evaluating | ||||||||||||||||||||
| 14(b). | Fit a Poisson Distribution to the following data which gives the number of doddens in a sample of clover seeds
| BTL-4 | Analyzing |
PART-C
| 1(a). | A disciplinary committee is formed from the staff of XYZ Company which has three departments Marketing, Finance and Production of the 10,5,20 members respectively. All departments have two female staff each. A department is selected at random and from which two matters are selected for the committee, What is the probability that both the team members are female? | BTL-6 | Creating |
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| 1(b). | In a bolt factory machines A, B, C manufacture respectively 25, 35 and 40 percent of the total. Of their output 5, 4 and 2 percent are defective bolts respectively. A bolt is drawn at random from the product and is found o be defective. What are the probabilities that it was manufactured by machines A, B or C? | BTL-2 | Understanding |
| 2(a). | State Bayes theorem and brief about its applications. | BTL-2 | Understanding |
| 2(b). | Out of 800 families with 4 children each, how many families would be expected to have (i) 2 boys and 2 girls (ii) at least 1 boy (iii) at most 2 girls (iv) children of both sexes? Assume equal probabilities for boys and girls. | BTL-1 | Remembering |
| 3. | Describe the classifications of probability ? | BTL-1 | Remembering |
| 4. | What are the applications of Normal distribution in statistics? | BTL-6 | Creating |
UNIT -II- SAMPLING DISTRIBUTION & ESTIMATION.
SYLLABUS: Introduction to sampling distributions, sampling distribution of mean and proportion, application of central limit theorem, sampling techniques. Estimation: Point and Interval estimates for population parameters of large sample and small samples, determining the sample size.
PART - A
| S.N 0 | QUESTIONS | BT Level | COMPETENCE |
|---|---|---|---|
| 1. | Define Sampling distribution of proportion. | BTL-1 | Remembering |
| 2. | Define Probable standard error. | BTL-1 | Remembering |
| 3. | Define standard error and mention its importance | BTL-1 | Remembering |
| 4. | Define central limit theorem | BTL -1 | Remembering |
| 5. | What is the role of central limit theorem in estimation and testing problems | BTL-6 | Creating |
| 6. | Define stratified sampling technique | BTL-1 | Remembering |
| 7. | Briefly describe the significance level. | BTL -1 | Remembering |
| 8. | Distinguish between parameter and statistic. | BTL -2 | Understanding |
| 9. | Define estimator, estimate and estimation. | BTL -1 | Remembering |
| 10. | Distinguish between point estimation and interval estimation | BTL-2 | Understanding |
| 11. | Mention the properties of a good estimator. | BTL-1 | Remembering |
| 12. | Define confidence coefficient. | BTL-1 | Remembering |
| 13. | What is the level of significance in testing of hypothesis | BTL-6 | Creating |
| 14. | Define confidence limits for a parameter | BTL-1 | Remembering |
| 15. | State the conditions under which a binomial distribution becomes a normal distribution | BTL -4 | Analyzing |
| 16. | If the random sample comes from a normal population, what can be said about the sampling distribution of the mean. | BTL-5 | Evaluating |
| 17. | An automobile repair shop has taken a random sample of 40 services that the average service time on an automobile is 130 minutes with a standard deviation of 26 minutes. Compute the standard error of the mean. | BTL-6 | Creating |
| 18. | What is a random number? How it is useful in sampling? | BTL-6 | Creating |
| 19. | A population has the numbers: 12, 8, 10, 30, 12, 16, 40, 5, 16, 24, 22, 31, 30, 16, 15. Draw a systematic sample of size 5. Find out its mean. | BTL-3 | Applying |
| 20. | How large sample is useful in estimation and testing | BTL -4 | Analyzing |
PART -B
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| 1(a). | A random sample of 700 units from a large consignment showed that 200 were damaged. Find (i) 95% (ii) 99% confidence limits for the proportion of damaged units in the consignment. | BTL-3 | Applying |
| 1(b). | A random sample of size 9 is obtained from a Normal population with mean 25 and if the variance 100 find the probability that the sample mean exceeds 31.2. | BTL -4 | Analyzing |
| 2(a). | In a normally distributed population, average income per household is Rs.20,000 with a standard deviation of Rs. 1,600. Find the probability that the sample mean will be between Rs.19,600 and Rs.20,200 in a survey of a random sample of 100 households. | BTL-6 | Creating |
| 2(b). | A university wants to determine the percentage of students who would accept proposed fees hike for improving facilities. The university wants to be 90% confident that the percentage is within2% of the true value. Find the sample size to achieve the accuracy regardless of the true percentage assuming the percentage of students accepting the increase in tuition fees to be 0.5. | BTL-6 | Creating |
| 3(a). | A bank has kept records of the checking balances of its customers and determined that the average daily balances of its customers is Rs.300 with a standard deviation of Rs. 48. A random sample of 144 checking accounts is selected. (i) What is the probability that the sample mean will be more than Rs. 306.60? (ii) What is the probability that the sample mean will be less than Rs. 308? | BTL-6 | Creating |
| 3(b). | From the question 3(a) (i) What is probability that the sample mean will between Rs. 302 and Rs. 308? (ii) What is probability that the sample mean will be atleast Rs. 296? | BTL-6 | Creating |
| 4(a). | Explain Stratified sampling technique and discuss how it is better | BTL -4 | Analyzing |
| than simple random sampling in a particular situation. | |||
| 4(b). | Discuss the standard error of proportion | BTL-2 | Understanding |
| 5. | Explain the methods of drawing simple random sample from a finite population. | BTL-4 | Analyzing |
| 6(a). | In a sample of 1000 citizens of India, 540 are wheat eaters and the rest are rice eaters. Can we assume that both rice and wheat equally popular in India at 1 % level of significance? | BTL-5 | Evaluating |
| 6(b). | A simple random sample of 144 items resulted in a sample mean of 1257.85 and standard deviation of 480. Develop a 95% confidence interval for the population mean | BTL-6 | Creating |
| 7(a). | A car dealer wants to estimate the proportion of customers who still own the cars they purchased 5 years earlier. A random sample of 500 customers selected from the dealer's records indicate that 315 customers still own cars that they were purchased 5 years earlier. Set up 95% confidence interval estimation of the population proportion of all the customers who still own the cars 5 years after they were purchased. | BTL-2 | Understanding |
| 7(b). | A movie maker sampled 55 fans who viewed his master piece movie and asked them whether they had planned to see it again. Only 10 of them believed that the movie was worthy of a second look. Find the standard error of the population of fans who will view the film a second time. Construct a 90% confidence interval for this population. | BTL-5 | Evaluating |
| 8(a). | From a population of size 600, a sample of 60 individuals revealed mean and standard deviation as 6.2 and 1.45 respectively. (i) Find the estimated standard error (ii) Construct 96% confidence interval for the mean. | BTL-3 | Applying |
| 8(b). | The age of employees in a company follows normal distribution with its mean and variance as 40 years and 121 years respectively. If a random sample of 36 employees is taken from a finite normal population of size 1000, what is the probability that the sample mean is (i) less than 45 (ii) greater than 42 and (iii) between 40 and 42? | BTL-6 | Creating |
| 9(a). | A firm wishes to estimate with an error of not more than 0.03 and a level of confidence of 98%, the proportion of consumers that prefer its brand of household detergent. Sales report indicate the about 0.20 of all consumers prefer the firm's brand. What is the requisite sample size? | BTL-5 | Evaluating |
| 9(b). | A random sample of 700 units from a large consignment should that 200 were damaged. Find (i) 95% (ii) 99% confidence limits for the proportion of damaged units in the consignment | BTL-3 | Applying |
| 10(a). | From a population of 500 items with a mean of 100 gms and standard deviation of This download link is referred from the post: RGUHS Pharma D Important Questions (Question Bank) |
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