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principles of managerial statistics

Questions and Answers of Principles Of Managerial Statistics

From a group of ten boys and eight girls, two pupils are chosen at random. Find the probability that they are both girls.
From a group of six men and eight women, five people are chosen at random. Find the probability that there are more men chosen than women.
From a bag containing six white counters and eight blue counters, four counters are chosen at random. Find the probability that two white counters and two blue counters are chosen.
From a group of ten people, four are to be chosen to serve on a committee. (a) In how many different ways can the committee be chosen? (b) Among the ten people there is one married couple. Find the
In a group of six students, four are female and two are male. Determine how many committees of three members can be formed containing one male and two females. (L)
Four persons are chosen at random from a group of ten persons consisting of four men and six women. Three of the women are sisters. Calculate the probabilities that the four persons chosen will: (a)
A touring party of 20 cricketers consists of nine batsmen, eight bowlers and three wicketkeepers. A team of 11 players must have at least five batsmen, four bowlers and one wicket keeper. How many
Find the number of ways in which ten different books can be shared between a boy and a girl if each is to receive an even number of books.
Four letters are picked from the word BREAKDOWN. What is the probability that there is at least one vowel among the letters?
Eight people sit in a minibus: four on the sunny side and four on the shady side. If two people want to sit on opposite sides to each other and another two people want to sit on the shady side, in
Disco lights are arranged in a vertical line. How many different arrangements can be made from two green, three blue and four red lights (a) if all nine lights are used, (b) if at least eight lights
A competition has a first prize, a second prize, a third prize and a fourth prize. Ten competitors enter this competition and the prizes are awarded for the first, second, third and fourth
The number of applicants for a job is 15. (C) Calculate the number of different ways in which six applicants can be selected for interview. The six selected applicants are interviewed on a particular
Each of seven children, in turn, throws a ball once at a target. Calculate the number of ways the children can be arranged in order to take the throws. Given that three of the children are girls and
To enter a cereal competition, competitors have to choose the eight most important features of a new car, from a possible 12 features, then list the eight in order of preference. Each cereal packet
Three letters are selected at random from the word SCHOOL. Find the probability that the selection (a) does not contain the letter O, (b) contains both the letters O.
How many even numbers can be formed with the digits 3, 4, 5, 6, 7 by using some or all of the numbers (repetitions are not allowed)?
OOOO Different coloured pegs, each of which is painted in one and only one of the six colours red, white, black, green, blue and yellow, are to be placed in four holes, as shown in the figure, with
(a) Calculate how many different numbers altogether can be formed by taking one, two, three and four digits from the digits 9, 8, 3 and 2, repetitions not being allowed. (b) Calculate how many of the
The positions of nine trees which are to be planted along the sides of a road, five on the north side and four on the south side, are shown in the figure.(a) Find the number of ways in which this can
A committee consisting of six persons is to be selected from five women and six men. (a) Calculate the number of ways in which the chosen committee will contain exactly two men. (b) Given that the
A committee of eight members consists of one married couple together with four other men and two other women. From the committee a working party of four persons is to be formed. Find the number of
Each time a table tennis player serves, the probability that she wins the point is 0.6, independently of the result of any preceding serves. At the start of a particular game, she serves fur cach of
A director of a company is selected at random. C denotes the event that the director's annual salary is more than 300 000. C' denotes the event that the director's annual salary is not more than 300
Newborn babies are routinely screened for a serious disease which affects only two per 1000 babies. The result of screening can be positive or negative. A positive result suggests that the baby. has
A penalty shoot-out in a game of hockey requires each of two players to take a penalty hit to try to score a goal. In a simple model, each player has a probability of 0.8 of scoring a goal, and
Forty 17 and 18-year old students are the only people present at a party. The numbers of male and female students of each age are given in the following table. 17-year old 18-year old Male 9 13
Each customer at a supermarket pays by one of cash, cheque or credit card. The probability of a randomly selected customer paying by cash is 0.54 and by cheque is 0.18. (a) Determine the probability
At an art exhibition seven paintings are to be hung in a row along one wall. Find the number. of possible arrangements. Given that three paintings are by the same artist, find the number of
A group of three pregnant women attend ante-natal classes together. Assuming that each woman is equally likely to give birth on each of the seven days in a week, find the probability that all three
The probability that for any married couple the husband has a degree is and the probability that the wife has a degree is . The probability that the husband has a degree, given that the wife has a
A bag contains four red counters, three blue counters and three green counters. A counter is drawn at random from the bag and not replaced. A second counter is then drawn at random from the bag.
A particular firm has six vacancies to fill from (C) 15 applicants. Calculate the number of ways in which these vacancies could be filled if there are no restrictions. The firm decides that three of
Laura has 12 friends, seven girls and five boys, all of whom she wants to come to her birthday party. However, she is only allowed to invite five of them. Not wishing to show any favouritism, Laura
A bag contains ten balls, of which four are red and six are blue. An experiment consists of drawing at random and without replacement three balls, one at a time, from the bag. (a) Draw a tree diagram
Ann, Barry and Clare are three students taking a multiple choice examination paper. For each question a student has to select the correct answer from five that are offered. For Question 1, Ann has no
The captain of a darts team is trying to arrange an evening match for next Monday, Tuesday, Wednesday or Thursday. He hopes that the leading players, A, B, C and D, will all be free on one of these
A coin is biased so that, on each toss, the probability of obtaining a head is 0.4. The coin is tossed twice. (a) Calculate the probability that at least one head is obtained. (b) Calculate the
The probabilities of events A and B are P(A) and P(B) respectively. P(A) = P(AB) = P(AUB)-q- Find, in terms of q (a) P(B), (b) P(A|B). Given that A and B are independent events, (c) find the value of
A questionnaire asks shareholders of a company to state whether they consider the chairman's salary to be too high, about right, or too low. Excluding shareholders who have no opinion, the
A school has three photocopiers A, B and C. On any given day the independent probabilities of a breakdown are 0.1 for A, 0.05 for B and 0.041 for C. For a randomly chosen day, calculate the
Every year two teams, the Ramblers and the Strollers, meet each other for a quiz night. From past results it seems that in years when the Ramblers win, the probability of them winning the next year
Two fair coins are tossed. Show the possible outcomes on a possibility space diagram and find the probability that two heads are obtained.
In a class of 20 children, 4 of the 9 boys and 3 of the 11 girls are in the athletics team. A person from the class is chosen to be in the 'egg and spoon' race on Sports Day. Find the probability
In a survey, 15% of the participants said that they had never bought lottery tickets or a premium bonds, 73% had bought lottery tickets and 49% had bought premium bonds. Find the probability that a
Events A and B are such that P(A) = 0.3, P(B) 0.4, P(A B) = 0.1. Find (a) P(An B'), (b) P(A'n B')
A group of 50 people was asked which of three newspapers, A, B or C they read. The results showed that 25 read A, 16 read B, 14 read C, 5 read both A and B, 4 read both B and C, 6 read both C and A
In a race in which there are no dead heats, the probability that John wins is 0.3, the probability that Paul wins is 0.2 and the probability that Mark wins is 0.4. Find the probability that (a) John
A card is drawn from an ordinary pack of 52 playing cards. Find the probability that the card is (a) a club or a diamond, (b) a club or a King.
When a die was thrown the score was an odd number. What is the probability that it was a prime number?
In a certain college 65% of the students are full-time students, 55% of the students are female, 35% of the students are male full-time students. Find the probability that (a) a student chosen at
A group of girls at a school is entered for Advanced Level Mathematics modules. Each girl takes only module M1 or only module M2 or both M1 and M2. The probability that a girl is taking M2 given that
A fair die is thrown twice. Find the probability that two fives are thrown.
Events A and B are independent and P(A) - }, P(A n B) = Find (a) P(B) (b) P(AUB).
The events A and B are such that P(A|B)-0.4, P(B|A)-0.25, P(An B)-0.12. (a) Calculate the value of P(B). (b) Give a reason why A and B are not independent. (c) Calculate the value of P(A n B').
In a group of 60 students, 20 study History, 24 study French and 8 study both History and French. Are the events 'a student studies History' and 'a student studies French' independent?
The events A and B are such that P(A) 0.45, P(B) 0.35 and P(AUB) -0.7. (a) Find the value of P(An B). (b) Explain why the events A and B are not independent. (c) Find the value of P(A|B).
The probability that a certain type of machine will break down in the first month of operation is 0.1. If a firm has two such machines which are installed at the same time, find the probability that,
The events A and B are independent and are such that P(A)-x, P(B)=x+0.2, and P(AB)=0.15. (a) Find the value of x. For this value of x, find (b) P(AUB), (c) P(A|B). (L
Three people in an office decide to enter a marathon race. The respective probabilities that they will complete the marathon are 0.9, 0.7 and 0.6. Assuming that their performances are independent,
Two ordinary fair dice, one red and one blue, are to be rolled once. (a) Find the probabilities of the following events: Event A: the number showing on the red die will be a 5 or a 6. Event B: the
The three events E,, E, and E, are defined in the same sample space. The events E, and E, are mutually exclusive. The events E, and E, are independent. Given that P(E)-3, P(E) and P(E, UE), find (a)
In a certain selection of flower seeds have been treated to improve germination and have been left untreated. The seeds which have been treated have a probability of germination of 0.8, whereas the
A manufacturer makes writing pens. The manufacturer employs an inspector to check the quality of his product. The inspector tested a random sample of the pens from a large batch and calculated the
Events X and Y are such that P(X), P(Y|X) = P(Y |X) - By drawing a tree diagram, find (a) P(Y) (b) P(XY)
When a person needs a minicab, it is hired from one of three firms, X, Y and Z. Of the hirings 40% are from X, 50% are from Y and 10% are from Z. For cabs hired from X, 9% arrive late, the
(a) Find the probability of obtaining at least one six when five dice are thrown. (b) Find the probability of obtaining at least one six when # dice are thrown. (c) How many dice must be thrown so
A witness reported that a car seen speeding away from the scene of the crime had a number plate that began with V or W, the digits were 4, 7 and 8 and the end letters were A, C, E. He could not
If a four-digit number is formed from the digits 1, 2, 3 and 5 and repetitions are not allowed, find the probability that the number is divisible by 5.
Ten pupils are placed at random in a line. What is the probability that the two youngest pupils are separated?
The letters of the word MATHEMATICS are written, one on each of 11 separate cards. The cards are laid out in a line. (a) Calculate the number of different arrangements of these letters. (b) Determine
The six letters of the word LONDON are each written on a card and the six cards are then shuffled and placed in a line. (a) Calculate the number of different arrangements. (b) Find the probability
Six bulbs are planted in a ring and two do not grow. What is the probability that the two that do not grow are next to each other?
One white, one blue, one red and two yellow beads are threaded on a ring to make a bracelet. Find the probability that the red and white beads are next to each other.
In how many ways can a hand of four cards be dealt from an ordinary pack of 52 playing cards?
Four letters are chosen at random from the word RANDOMLY. Find the probability that all four letters chosen are consonants.
A team of four is chosen at random from five girls and six boys. (a) In how many ways can the team be chosen if (i) there are no restrictions; (ii) there must be more boys than girls? (b) Find the
If a diagonal of a polygon is defined to be a line joining any two non-adjacent vertices, how many diagonals are there in a polygon of (a) five sides, (b) six sides, (c) n sides?
Three letters are chosen at random from the word BIOLOGY. Find the number of possible selections.
Seven cards, labelled A, B, C, D, E, F, G, are thoroughly shuffled and then dealt out face upwards on a table. Find the probabilities, giving each as a fraction in its simplest form, that (a) the
A die is biased so that, when it is rolled, the probability of obtaining a score of 6 is. The probabilities of obtaining each of the other five scores 1, 2, 3, 4, 5 are all equal. Calculate the
A factory has three machines A, B, C producing large numbers of a certain item. Of the total daily production of the item, 50% are produced on A, 30% on B and 20% on C. Records show that 2% of items
How does core risk differ from non- core risk?
What are different types of risks a financial institution/ bank can face in their business?
What is the difference between ALM and liquidity risk?
What is the difference between market risk and credit risk?
Why statistical analysis is important for risk management? or how operational risk is different from credit risk?
What is the difference among EAD, LGD, and PD?
What is yield curve risk?
What is BLET matrix?
How RCSA is different from KRI?
What is RAPM system? How does it work in an organization?
What is the role of descriptive statistics in research? Suppose you have data on the price, weight, mileage rating, and repair record of 22 foreign and 52 domestic automobiles. You want to summarize
Do you think that quantitative and qualitative data have similar applications in risk- related empirical research?
Why data cleaning and sorting are important in risk analysis?
What the key differences are between cross- sectional and time series data?
Why panel data have more observations?
Do you think lower degrees of freedom in data analysis would lead to biased opinion about the results?
Is it true that the width of the confidence interval measures how uncertain we are about the unknown population parameters?
Is it true that when the Gini Coefficient for distribution of exposure in a loan portfolio approaches 1, then the concentration risk is very high?

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