Statistics Questions and Answers May 30, 2018

Question Four (20 Marks) a) A student prepares for an exam by studying a list of 15 problems. She can solve six of them. For the exam, the instructor selects 8 questions at random from the list of fifteen. What is the (6 Marks) probability that the student can solve at least four problems on the exam b) Suppose that a system contains a certain

1. You are thinking of moving to live in Nakuru. As part of your research into what its like to live in Nakuru you have collected the following sets of data ii) the maximum daily temperature each day since 1 January 2003 whether or not it rained for each day since 1 January 2003 the number of cyclists injured in road accidents since 1 January

7. The classification of stochastic models according to discrete or continuous time variable with discrete or continuous state space gives rise to a fourway classification. Give four practical problems, one of each type, of stochastic models which may be used to model observed processes. 8. Find the generating function for the given sequences i)

11. Let X be a discrete random variable. Find the generating function for the following sequences i) qP(X

0 1. Consider a branching process with Z 1 and let Y ZZ...Z, be the total progeny. Derive the pgf R,(s) of the total progeny and hence find its i) Mean ii) Variance (when 1) 2. Calculate the PGF of the second generation. i) ii) distribution of the second distribution iii) probability of extinction by third generation iv) probability of

4. A population starts off with just one female. Each female lives for a fixed time I and then dies. The number of female off springs of a single female is given by the following probability distribution x 0 1 pr(x) 0.2 0.4 2 3 0.3 0.1 i) Find the probability distribution of the second generation. ii) Determine the probability of extinction by

1. A Markov chain X, X1, X2,... on states 0, 1, 2 has the transition probability matrix T and that Po 0.4 P 0.4 and p 0.2. Find 2. Pr(X1, X31X 0) Pr(X 1,X21X 0) Pr(X1, X 1, X 2) Pr(X1,X 2, X 0) 0 i) ii) iii) iv) v) E(X3) 0.6 0.3 0.1 a) T0.3 0.3 0.4 0.4 0.1 0.5 0.1 0.1 0.8 b) T0.2 0.2 0.6 0.3 0.3 0.4 0.3 0.2 0.5 c) T0.5 0.1 0.4 0.5 0.2 0.3

2. A Markov chain X, X1, X2,... on states 0, 1, 2 has the transition probability matrix T. Find i) Pr(X31X 0) ii) Pr(X 2X 1) 0 iii) Pr(X3 2X 0) iv) 0 Pr(X 2) if X 1 0.6 0.3 0.1 a) T0.3 0.3 0.4 0.4 0.1 0.5 0.1 0.1 0.8 b) T0.2 0.2 0.6 0.3 0.3 0.4 0.3 0.2 0.5 c) T 0.5 0.1 0.4 0.5 0.2 0.3 0.1 0.2 0.7 d) T0.2 0.2 0.6 0.6 0.1 0.3

3. Determine the limiting distribution if 0.6 0.3 0.1 a) T 0.3 0.3 0.4 0.4 0.1 0.5 0.1 0.1 0.8 b) T0.2 0.2 0.6 0.3 0.3 0.4 0.3 0.2 0.5 c) T0.5 0.1 0.4 0.5 0.2 0.3 0.7 0.2 0.1 d) T 0 0.4 0.6 0.5 0 0.5 4. Suppose that a production process changes state according to a Markov process whose transition probability matrix is given by 0.3 0.5 0 0.2 0.5

5. An insurance company classifies its auto insurance policyholders in the categories high, intermediate, or low risk. In any given year, a policyholder has no accidents with probability 0.6, one accident with probability 0.2, two accidents with probability 0.1, and more than two accidents with probability 0.1. If you have no accidents, you are

7. For the following Markov chains, determine i) Which states are transient and which are recurrent. ii) Which states form a closed subset iii) Whether it is irreducible or not iv) Period of each state 2 00 1 0 0 0 a) T 0 3, 0 4 0 ( 0 b) T 4 4 4 0 4 ) 00000 ( 23 0 3 1 00 c) T 0 13 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 000 01 0 0 0 001 0 0 00,d) T

1. Fred is giving out samples of canned dog food. He makes calls door to door, but he leaves a sample (one can) only on those calls for which the door is answered and a dog is in residence. On any call the probability of the door being answered is 34, and the probability that any household has a dog is 23. Assume that the events Door answered and

5. Messages arrive at a telegraph office as a Poisson process with mean rate of 3 messages per hour. What is the i) ii) Probability that no messages arrive during the morning hours 800 A.M. to noon Distribution of the time at which the first afternoon message arrives 6. Suppose that customers arrive at a facility according to a Poisson process

9. Customers enter a store according to a Poisson process of rate 6 per hour. Suppose it is known that but a single customer entered during the first hour. What is the conditional probability that this person entered during the first fifteen minutes 10. Customers arrive at a service facility according to a Poisson process of rate 25 per hour.

The substance weight of a type of paper follows a normal distribution with a mean of 40 pounds per square inch and a standard deviation of 3 pounds per square inch. a. What is the probability that the substance weight of a sample is greater than 45 pounds per square inch b. If the specifications require the substance weight to exceed 37 pounds per

A man owes P10,000 with interest at 6% payable semi-annually. What equal payments at the beginning of each 6 months for 8 years will discharge his debt?

V. A focus group of 10 adults was chosen to evaluate the performance of candidate during a presidential debate. They were instructed to rate the candidate on two characteristics, knowledge and delivery, using a scale of 1 (poor) to 10 (superior). The ratings given the candidate were as follows Rater Knowledge Rating Delivery Rating I J ABCDEROHLS

Question (Relationship between sdomain and zdomain)(Draw both by hand and Matlab mfile) In figure 1, constant damping ration curve, constant frequency curve and constant time constants are given. Draw the equivalents of given curves in zdomain by hand and also via Matlab.( T 0.3 sec ) splane 45 25 splane splane js 25 splane js 15 25 35 25 (c) (d)

The probability of an archer hitting a target is (47). (i) If the archer fires 9 arrows, calculate the probability he will hit the target 5 times, correct to two decimals. (ii) Calculate the probability that his 5th hit will occur on the 9th arrow, correct to two decimal places.

The probability of event E is 0.54, the probability of event F is 0.38, and the probability of both is 0.2. What is the probability of either E or F?

3.39 The file Tax contains the quarterly sales tax receipts (in thousands) submitted to the comptroller of the Village of Fair Lake for the period ending March 2013 by all 50 business estab lishments in that locale 10.3 11.1 9.6 9.0 14.5 13.0 6.7 11.0 8.4 10.3 8.0 11.2 7.3 5.3 12.5 8.0 11.8 8.7 11.1 10.2 11.1 9.9 9.8 11.6 15.1 12.5 10.0 12.9 9.2

1.(LSAT)The LSAT (a test taken for law school admission) has amean score of 151with astandard deviation of 9and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of9students at a time. A larger organization teaches classes of25students at a time. Both organizations publish the mean scores of all

C Confidence level Example 95 Using BETWEEN in Statcrunch Degrees of freedom 11 Example 95 11 Using Standard in Statcrunch 90 17 98 88 95 7 99 102 Critical value 2.201 for a 95 CI for Critical value 2.2009 for a 95 CI for f(x) 0.4 0.3 0.2 0.1 0 f(x) 0.4 0.3 0.2 0.1 x T Distribution DF11 P(X2.2009852) 0.975 t T Distribution DF11 P(2.201x2.201)

3.Cattle Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of 11 pounds. Some students wrote the following conclusions. Did anyone

5. See accompanying dataset Flights on time 2016 Two questions What are the chances your flight will leave on time Will your flight get you to your destination on time The Bureau of Transportation Statistics of the U.S. Department of Transportation publishes information about airline performance. Below are histograms for the percentage of flights

6., 17 Wrong direction An IpsosReuters poll of 2214 U.S. adults voters in April and May 2017 asked a standard polling question of whether the United States was headed in the Right Direction or was on the Wrong Track. 54 said that things are on the wrong track vs. 33 who said right direction. a) Calculate the margin of error for the proportion of

7. Conclusions A catalog sales company promises to deliver orders placed on the Internet within 3 days. Followup calls to a few randomly selected customers show that a 95 confidence interval for the proportion of all orders that arrive on time is 88 6 What does this mean Are these conclusions correct YesNo. Between 82 and 94 of all orders arrive

9. Mislabeled seafood, second course A Consumer Reports study similar to the one described above found that 12 of the 22 red snapper packages tested were a different kind of fish. 1. Are the conditions for creating a confidence interval satisfied Explain. 2. Construct a 95 confidence interval. 3. Explain what your confidence interval says about

5.Calculate the recoil energy of the technetium atom as a result of photon emission in the isomeric transition 99mTc4399Tc43 Y.

. Write any two uses of statistics. 2. What is secondary data 3. Define classification of data. 4. What is class interval 5. What is Pie Diagram 6. What is Frequency Polygon 7. What is Weighted Arithmetic mean 8. What are various absolute measures of dispersion 9. What is mean deviation

13. What are the functions of statistics 14 Explain the importance of Data. 15 Explain the Use of graph. 16. What are the Features of ogives 17. What are the Points to be considered while selecting an average 18. Calculate 5 yearly moving average of the number of students studying in an engineering college from the following data. Year 2000 2001

22 Compute the median from the following data. 5069 7089 90109 110129 130159 Wages (Rs.) No. of workers 18 75 21 10 41 23 From the following data calculate standard deviation. Marks 24 28 32 36 40 44 48 No. of students 12 24 36 52 32 20 16 24. Represent the following data of family B by a pie diagram. Food Clothing Rent Entertainment Education

Chad's Pottery Barn memiliki cukup tanah liat untuk membuat 24 vas kecil atau 6 vas besar. Ia hanya memiliki cukup campuran pelapis khusus untuk melapisi 16 vas kecil atau 8 vas besar. Misalkan X = jumlah vas kecil dan X2 = jumlah vas besar. Vas yang lebih kecil dijual seharga $3 masing-masing, dan vas yang lebih besar masing-masing dijual seharga

1. Amount of money which equal to series of payments in future (a) nominal value of annuity (b) sinking value of annuity (c) present value of annuity (d) future value of annuity 2. Process of loan repayment by installment payment is classified as (a) amortizing loan (b) depreciation loan (c) appreciation loan (d) appreciation of investment 3.

1. Which of the following statement is true? (a) Statistics is derived from the French word statistic (b) Statistics is derived from the Latin word status (c) Statistics is derived from the Italian word statita (d) None of these 2. Class interval is measured as: (a) The sum of the upper and lower limit (b) Half of the sum of lower and upper limit

A new study by Square Trade indicates that smartphones are 50% more likely to malfunction than simple phones over a 3-year period. Of smartphone failures, 30% are related to internal components not working, and overall, there is a 31% chance of having your smartphone fail over 3 years. Suppose that smartphones are shipped in cartons of N=50

National College Health Assessment Survey The following exercise uses data on college students collected from the American College Health Association National College (a) did more males or females answer the survey or did approximately equal numbers of males and females participate? is graph(a) or (b) more helpful to answer this question? (b) did

The time required to pass through security screening at the airport can be annoying to travelers. The mean wait time during peak periods at Cincinnati/Northern Kentucky International Airport is 12.1 minutes. a) What is the probability it will take less than 10 minutes to pass through security screening during a peak period?

The radio music listener market is diverse listener formats might include adult call temporary ,album rock,top 40 oldest,rap country and western classical and jazzy in targeting audiences market researchers need to be concerned about the ages of the listeners attracted to particular formats.suppose a market researchers surveyed a sample of 170

A manufacturing company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars). State of Nature Decision Alternative Low 1

Compute the 35th percentile, the 55th percentile,Q1, Q2, and Q3 for the following data (16, 28 ,29, 13,17,20,11,34,32,27,25,30,19,18,33).

A tablet has 4 choices for an operating system, 3 choices for a screen, 4 choices for a processor, 6 choices for memory size, and 3 choices for a battery. How many ways can you customize the tablet?

x1 0, X2 0 937 16.0 KBS il 60 5. A manufacturing firm produces diesel engines in four citiesPhoenix, Seattle, St. Louis, and Detroit. The company is able to produce the following numbers of engines per month. Plant 1. Phoenix 2. Seattle 3. St. Louis 4. Detroit Productio n 5222 20 Three trucking firms purchase the following numbers of engines for

Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty. (a) If 11 people are called for jury duty, what is the probability that all 11 will be available to serve on the jury? (Round your answer to three decimal places.) (b) If 11 people are called

Clear Mountain State Student Survey The Student News Service at Clear Mountain State University (CMSU) has decided to gather data about the undergraduate students who attend CMSU. They create and distribute a survey of 14 questions and receive responses from 111 undergraduates 1. At the 0.05 level of significance, is there evidence of a difference

As a result of a court settlement, an accident victim is awarded $1.8million. The attorney takes one-third of this amount, another third is used for immediate expenses, and the remaining third is used to set up an annuity. What amount will this annuity pay at the beginning of each quarter for the next6years if the annuity earns7.3%, compounded

The Economic Order Quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model are holding cost per unit, ordering cost and the cost of goods ordered. The assumptions for that model are only a single item is considered the entire quantity ordered arrives at one time the demand for the

Each state collects information on every birth that occurs within its borders. The following data give the 2008 birth rates (number of births per 1000 people) for all of the 56 counties in the state of Montana. 12.2 7.7 3.1 14.5 7.8 13.6 8.8 10.9 8.9 14.7 9.6 14.2 14.9 18.3 22.8 5.4 5.6 19.6 8.2 9.9 14.7 13.7 10.3 9.7 9.8 8.6 9.4 14.1 12.3 10.5