1.It is estimated that during any one hour period, an average of 10 Internet users visit the
website of Sport-Equip Ltd,
of Sport-Equip Ltd, a company that sells sports equipment. Some of the users
who visit the website end up buying sports equipment from the website while others are
simply browsing in order to obtain product information.
(a) Clearly explain and justify which probability distribution you would use to
describe the number of Internet users who visit the website of Sport-Equip Ltd
in a one hour period. [There is no need to calculate any probabilities for this part
of the question]
(b) What is the probability that during any half-hour period, there will be less than 3
visitors to the website?
(c) What is the probability that during any two-hour period, there will be more than
15 visitors to the website?
(d) If a user has just visited the website, find the probability that the website will
have another visitor within the next 10 minutes. In your answer, state the
probability distribution you have used and explain your choice.
(e) It is estimated that 40% of Internet users who visit Sport-Equip Ltd’s website
buy a product from the company. If 100 users visit the website over a given
period of time, find the probability that more than 50 of them will buy a product
from the company. In your answer, state the probability distribution you have
used and explain your choice
2.A lock can be opened by inputting the correct sequence of four digits in the correct order, regardless of the
ss of the previous inputs. If the lock has buttons representing the digits 0-9 then there are 10000 possible combinations from 0000-9999. In class, we indicated that no less than 10003 digits must be pressed to test every possible four digit sequence.
Is there a sequence of length 10003 that tests all possible combinations. If so, this sequence must be given to me in your write up as well as an explanation on how you came up with this sequence.
If there is no sequence of length 10003 that tests all possible combinations, can you come up a sequence with less than the maximum number (40000) which tests all possibilities? How did you come up with this sequence?
3.11. In a game, you draw thirteen cards with replacement from a deck of playing cards. If you draw any
y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game?
12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX?
13. The following are probability distributions for two random variablesX,Y.
(a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y?
14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls?
15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?
4.The unit price of market goods is $1. Each person has 8 hours to work each day.
Another couple, Sylvan and
van and Alex, have the same productivities: Sylvan is identical to Rajan, while Alex
and Esther are identical.
Esther and Rajan both engage in market work. Sylvan works full time at home, so only Alex works in the
a) Given this information, which couple has the higher opportunity cost of home produced goods?
Explain how you determined this. You can add a diagram if that helps, but you are not required
to include one.
b) Can you determine which couple has the higher utility? Explain why or why not.
Suppose now that value of market production for both Alex and Esther increased to $12/per hour.
c) Explain the change in the household joint production possibility frontier generated by this
d) Explain what would happen to each couple’s choice of both household and market produced
goods, using an analysis by means of income and substitution effects.
e) What changes in time allocation for each couple that would be necessary to produce and
consume this new bundle? Briefly explain your reasoning.
A vital area of research is the identification of the correct statistical test to answer your research question.
Final Mission: You
your research question.
Final Mission: You will use the given dataset to develop a research question, create background on the topic related to the research question, and complete an analysis of the data to answer that research question.
➢ Use no more than 12 slides with a voice-over description for each slide. You may be creative with background and animation for the slide show but remember that it is the content that is most important (and animation, etc. can greatly increase your file size).
➢ Include an introductory slide that states your name, credentials, and title of your presentation.
➢ Present your research question.
➢ Identify the appropriate statistical test to answer the research question.
o Identify your variables of interest.
o Identify how they are measured and match them to the appropriate statistical test.
➢ Identify and evaluate appropriate assumptions to meet the test.
o Each statistical test comes with a set of assumptions that must be met in order to use the test; conditions that must be satisfied before using the test.
o Explain the assumptions and show how they have been met as well as how you would “fix” them if they were “broken.”
➢ Provide a justification for all the choices you made in the decision of which statistic to use and explain the necessary tests associated with it in terms someone not familiar with it would understand.
➢ Use APA format for any citations within the PowerPoint.
6.You are given a set of five and a set of seven contiguous boxes as shown in the figures above.
task is to move all the reds from the left to the right and all the blacks from the right to the left. The middlebox is empty to allow moves.
The moves follow strict rules.
Rule # 1: the reds can only move to the right and the blacks can only move to the left. No backward moves are allowed
Rule # 2: Equally applicable to the black and the reds, each dot can only move one step forward in the box in front of it is empty, and can skip the contiguous box is occupied by a different colored dot to the following box if empty.
While moving your pieces, carefully record all the moves you made. Start first with the 5-boxes set, then the 7-boxes set
Try the same rules for a 9-boxes set and then for an 11-boxes set. Record all your moves on paper
Examine all four cases and find a pattern that relates the number of moves to the number of dots. Explain how you arrived at this conclusion
Create a general formula that will give the number of moves based on the number of dots regardless of how many dots you have.
7.XYP (Ltd) embarks on a project to construct the townhouse in gauteng. They have requested you to draft a budget
ft a budget proposal in order for them to go and seek funding. The management team supplies you with the following information.
The company will not generate any income for the first 3 months of the year (jan - march) on the 4th month the company will generate sales of R500 000.00 thereafter the company sales will increase by 10% until December.
Salaries will be R85 000.00 a month from the beginning of the year. There will be increase of 7% which will only be applicable as if the sixth month. Staff bonus will be payable in December and will amount R28 000
Stationary printing expenses are estimated to be R10 000. 00( vat excluded) every month.
Telephone expenses in January are expected to be R5 500.00(vat excluded) and will increase by 5% every month.
Rent will be payable from the 3rd month at a cost of R 20 000.00. There will be decrease of 5% from August to the end if the year and the company will be given a rental discount of 10% in December.
Return on the investment will be as follows: april R90 000.00 August and September will be R80 000.00 december R150 000.00 all returns will be taxable according appropriate tax standards.
Draw a cash budget for XYP (pty) Ltd for the year ending 31 December 2018 (30)