# NOUN TMA STT205 STATISTICS FOR MANAGEMENT SCIENCE 1

In a survey of companies, it was found that 45 were in the mining sector, 72 were in the financial sector, 32 were in the IT sector and 110 were in the production sector. What is the likelihood that a randomly selected company is either a mining company o Answer: (D) 0.297 Hypergeometric distribution has parameters Answer: 2 if (0A{n} extrm{C}_{12}={}A{n} extrirKCHô}), the value of n is Answer: 18 Suppose that a histogram of a data set is approximately symmetric and \ Answer: (b) 68 The mean of 10 observations is 10 All the observations are increased by 10%. The mean of increased observations will be: Answer: 11 Consider probability distribution as standard normal, if value of 1% is 75, value of x is 120 with unknown standard deviation of distribution then value of z-statistic Answer: (d) will be positive If a value represents the 95th percentile, this means: Answer: 95% of all values are below this point If X= {1, 2, 3, 4, 5} and Y= {2, 4, 5, 6, 8} then Y-X equals to Answer: c: {6, 8} The mean of 10 observations is 10. All the observations are increased by 10%. The mean of increased observations will be: Answer: 10 If value of x for normal distribution is 35, mean of normal distribution is 65 and standard deviation is 25 then standardized random variable is Answer: (b) -1.2 Consider probability distribution as standard normal, if value of AZÂ’/i is 75, value of x is 120 with unknown standard deviation of distribution then value of z-statistic Answer: will be positive In a given sports activity, the annual rate of accidents is of about 4 per thousand people. An insurance company has 3000 insured clients that practice such sports activity. A good approximation of the number of accident compensations the insurance company will have to pay in a given year is given by the distribution Answer: poisson (âzâ» = 12) In a group of 6 boys and 44 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? Answer: b: 209 The number of clients that enter a given store each hour follows a Poisson distribution with mean 3.25. We assume independence between the diÂ-Â-«â,-*erent hours. The probability that in a given hour exactly 5 clients enter the store is? Answer: 0.1172 The number of apples sold on a particular day by a fruit seller are 2, 4, 7,10, 10,10, 12,12,14,15* Determine the value at the first quartile Answer: (B) 7 Of 12 accounts held in a file, four contain a procedural error in posting account balances* If an auditor samples three accounts randomly, what is the probability that at least one will contain the error? Answer: (A) 0*75 A principal of N1000 is invested at an 8* annual rate of interest* What will be the accrued interest after 6 years? Answer: (A) N586*87 In binomial distribution, formula of calculating standard deviation is Answer: square root of npq 2600 applications for home mortgage are received by a bank and probability of approval is 078 then standard deviation of binomial probability distribution is Answer: c: 446.16 If value of failure in binomial probability distribution is 0.70 and success is 0.30 and number of values in distribution are 7 then moment coefficient of kurtosis is Answer: b: 0.18 The percentage increase in the prices of five items (A, B, C, D and E) are respectively 15*. 35*. -10* -7* and 12** What is the mean percentage change? Answer: (B) 9* The probability of success changes from trial to trial in Answer: binomial distribution If z-score of normal distribution is 2.5, mean of distribution is 45 and standard deviation of normal distribution is 3 then value of x for a normal distribution is Answer: c: 37.5 if W(öA{n}\\textrm{C}_{12}= 0A{n}\\textrm{C}_{6}\\), the value of n Answer: (d) 18 The population of primary school pupils in the state of the country to allow the Federal Government plan for the primary education is an example of data Answer: primary An insurance company is considering the addition of major-medical coverage for a relatively rare ailment* The probability that a randomly selected individual will have the ailment is 0*001, and 3,000 individuals are included in the group that is insured* What's the probability that no one in this group of 3,000 people will have this ailment? Answer: (D) 0*0498 Find the value of v if vC3 = 35 Answer: (D) 7 If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then (P(Acup B)) Answer: zero if the probability of any page in a financial book containing an error is 0*005, what is the probability that at most three pages of its 400-page book are with errors? Answer: (C) 0*857 The hourly patronage of a restaurant is an example of variable Answer: quantitative The number of apples sold on a particular day by a fruit seller are 2, 4, 7,10, 10,10, 12,12,14,15* Determine the value at the 30th percentile Answer: (D) 8*5 If 10* of the bolts produced by a machine are defective, what is the probability that out of 5 bolts chosen at random at least 2 will be defective? Answer: (B) 0*08866 If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then (P (Acap B)) Answer: 0.8 If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then \\(P(A\\cup B)W) = Answer: (C) 0.8 Of 100 individuals who applied for database administrator positions with a large firm during the past year, 40 had some prior work experience (W), and 30 had a professional certificate (C)* However, 20 of the applicant«; had both work experience and a certifie and thus are included in both of the col What is the probability that a random ct )sen applicant had either work experience oi certificate but not both? Answer: (B) 0*3 A researcher is interested in the travel time of Utrecht University students to college A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study the mean of 16.7 minutes is an example of a(n) Answer: statistic Suppose that 40 percent of the employees in a large firm are in favor of union representation, and a random sample of 10 employees are contacted and asked for an anonymous response* What is the probability that fewer than half of the respondents will be in favor of union representation? Answer: (C) 0*633 Consider probability distribution as standard normal, if value of ? is 75, value of x is 120 with unknown standard deviation of distribution then value of z-statistic Answer: (d) will be positive Of 300 business students, 100 are currently enrolled in economics and 80 are currently enrolled in business statistics* These enrollment figures include 30 students who are in fact enrolled in both courses* What k the probability that a randomly chosen student will be enrolled in either econor. (E) or business statistics (B)? Answer: (C) 0*5 If X= {1. 2, 3,4, 5} and Y= {2, 4, 5, 6, 8} then \\(Y-X\\) equals to Answer: (c) {6, 8} In a survey of companies, it was found that 45 were in the mining sector, 72 were in the financial sector, 32 were in the IT sector and 110 were in the production sector If a company is selected at random, what is the probability that this company is not in tf production sector? Answer: 0575 In studying the nutritional well-being of pupils in a primary school, the a pupil in the school Answer: entity Â If value of x for normal distribution is 35, mean of normal distribution is 65 and standard deviation is 25 then standardized random variable is Answer: -1.2 If X *** Po(k) a poisson random variable with parameter k, then which of the following is false* mean equal 2k Answer: (D) 2k is the mean There are 6 pupils and 4 cats In how many can they be seated in a row so that no cats sit together Answer: 6! x 7p4 How many four-digit numbers can be formed with the 10 digits if the last digit must be zero and repetitions are not allowed? Answer: (B) 504 If A and B are mutually exclusive events with P(A) = 03 and P(B) = 0.5, then \(P (A\cap B)\) - Answer: zero For what value of m is m+1 P3 = mP4? Answer: (C) 5 The mean, median, mode and the standard deviation of a set of numbers are 2360, 2340,1980 and 650 respectively, what is the value of first coefficient of skewness? Answer: (B) 0*5846 The probability distribution function of weekly share sales X was **f(x)=*left* {*begin{matrix}*frac{3}{2X1 -x*2) * 0*leq x*leq 1*0* otherwise *end{matrix}*right*** what is the expected value of X? Answer: (D) (3*8) There are 6 pupils and 4 cats. In how many can they be seated in a row so that no cats sit together Answer: 6 ! 6 â/â€” 6 ! 6 The average expenditure per week of four items (A, B, C, D ) are N20, N30, N30 and N50 respectively, if the percentage increase in the prices of the items are 10*, -6*, -8* and 20** What is the mean percentage change by weighing the percent increa each item by the average amount per w ?ek spent on that item Answer: (B) 6* The size of a family is an example of a variable Answer: continuous Â,Â A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study the mean of 16.7 minutes is an example of a(n) Answer: parameter In a survey of companies, it was found that 45 were in the mining sector, 72 were in the financial sector, 32 were in the IT sector and 110 were in the production sector. If a company is selected at random, what is the probability that this company is not Answer: (D) 0.575 If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then \\(P (AWcap B)W) = Answer: (C) zero If quartile range is 24 then quartile deviation is Answer: 48 If mean of binomial probability distribution is 25 then mean of Poisson probability distribution is Answer: c: 25 if \(0A{n}\textrm{C}_{12}= 0A{n}\textrm{C}_{6})\, the value of n is Answer: 18 In how many ways can 14 objects be split into 3 groups consisting of 2, 5 and 7 objects respectively Answer: (B) 72072 variable is the variable that can only assume whole numbers Answer: discrete Two cards are drawn from a deck of 52 cards* Find the probabilities of the event that the first card is a king and the second a figure Answer: (A) 0*0165 Which of the following statements is always correct? Answer: mean = median = mode The number of apples sold on a particular day by a fruit seller are 2, 4, 7,10, 10,10, 12,12,14,15* Determine the value at the second decile Answer: (B) 5*5 Colours of fruits and taste of some brands of a biscuit are examples of variable Answer: qualitative Suppose that three cards are chosen randomly from a playing deck of 52card s, but that after each selection the card is replaced and the deck is shuffled before the next selection of a card* What is the probability that all three cards are aces' Answer: (D) 0*0005 There is a 90 percent chance that a particular type of component will perform adequately under high temperature conditions* If the device involved has four such components, determine the probahilitv that the device is inoperative because exactly one of the four components fail*. Answer: (A) 0*2916 is used extensively to control and analyse stock level such as minimum, maximum and reorder levels. Answer: statistics Consumer products are those products bought by consumers for personnal consumption Answer: (D) current If a man purchases world cup raffle ticket, he can win a first prize of N60000 or a second prize of N35000 with probabilities 0*0005 and 0*0003* what is a fair price to pay for the ticket? Answer: (A) N40*50 Tail or head, one or zero and girl and boy are examples of Answer: b: complementary events In a survey of companies, it was found that 45 were in the mining sector, 72 were in the financial sector, 32 were in the IT sector and 110 were in the production sector. If a company is selected at random, what is the probability that this company is not in tt production sector? Answer: 0.596 variable is a variable whose values are given as numerical quantities Answer: quantitative In how many different ways can the letters of the word YCORPORATIONY be arranged so that the vowels always come together? Answer: (d) 50400 A variable that is not measurable in numerical form or that cannot be counted is called variable Answer: qualitative The number of clients that enter a given store each hour follows a Poisson distribution with mean 3.25. We assume independence between the di?erent hours. The probability that in a given hour exartiv 5 clients enter the store is? Answer: (b) 0.1172 Young ladies have normally distributed weights with mean equal to 70gm and standard deviation equal to 3gm, what percent are between 68 and 73gm? Answer: (C) 0*5889 In a survey of companies, it was found that 45 were in the mining sector, 72 were in the financial sector, 32 were in the IT sector and 110 were in the production sector. What is the likelihood that a randomly selected company is either a mining company or IT company Answer: 0.308 If a bag contains three fruits, 16 percent are apples, 30 percent are oranges and 20 percent some other fruit that is neither oranges nor apples then probability of selecting an orange randomly is Answer: a: 0.3 Find the probability that during one particular minute there will be 4 or fewer phone calls, if between the hours 10 and 12noon, the average number of phone calls coming into the company is 2*5 Answer: (B) 0*8911 In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? Answer: d: 50400 The probability of getting an answer to question is 0*6* what is the probability of a student getting 3 out of 5 questions Answer: (C) 0*3456 Which of the following sets of figures has the greatest variability (range)? Answer: a: -2, 5, 8,12 Â/â€sÂ,Â A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study the mean of 16.7 minutes is an example of a(n) Answer: (B) Statistic If A and B are mutually exclusive events with P(A) = 03 and P(B) = 0.5, then \(P(A\cup B)\) Answer: 08 The mean and the median wages of a group of workers are N350 and N340 respectively, what is the modal wage? Answer: (B) N320 During one month the ratio of millet prices to corn was 4*5, whereas during the next month the ratio was 2*5* find the arithmetic mean of the ratios of com to millet for the 2- month period* Answer: (C) 0*3111 Management uses to make forecast about the sales and labour cost of a firm Answer: statistics Given that group of girls and boys exist in equal number, and assuming that 5* of the boys are colour blind and that 10* of the girls are colour blind, evaluate the probability that, having drawn a colour-blind person this is a female Answer: (B) 0*6666 The number of clients that enter a given store each hour follows a Poisson distribution with mean 3.25. We assume independence between the din€erent hours. The probability that in a given hour exartiv 5 clients enter the store is? Answer: (b) 0.1172 Data based on workers salary is given as: 2500, 2700, 2600, 2800, 2200, 2100, 2000, 2900, 3000, 2800, 2200, 2500, 2700, 2800, 2600; and number of classes desired is 10 then width of class interval is Answer: 100 Suppose that a histogram of a data set is approximately symmetric and Answer: 68