Lendright is considering investing in a proposed merger in which a company producing torches is negotiating with a company for the supply of torch bulbs. Lendright has been asked to help assess how the bulb company needs to plan its production to meet the needs of the torch company by using that company’s quarterly sales figures over the past three years to forecast future demand. The sales figures are as follows:
(a) Using the moving average technique find the trend observations and the seasonal variation.
(b) Fit a least squares regression line to the trend observations.
(c) Use this trend regression line and your estimates of the seasonal variation factors to forecast future demand for the four quarters of year 4 for torches.
Q45:
Write down the theoretical probabilities that Stage-it would apply to outcomes from the following events in its gaming division:
(a) rolling a dice and getting a 2;
(b) rolling a dice and not getting a 3;
(c) rolling a dice and getting an odd number;
(d) rolling a dice and getting a 2 or a 3;
(e) drawing an ace from a pack of cards;
(f) drawing a card from a pack of cards and not getting a diamond;
(g) rolling a dice and getting a number less than 7.
Q46:
The following probabilities are relevant decisions for Stage-it’s gaming division. Two unbiased dice are thrown. Their scores are added to make a total between 2 and 12.
(a) There are 36 possible totals as indicated in Figure 5.1. Complete the table. (b) Write down the theoretical probability of throwing a total of:
(i) 2;
(ii) 3;
(iii) 4;
(iv) 6;
(v) 7;
(vi) 8;
(vii) 10;
(viii) 12.
(c) What is the theoretical probability of not getting a total of 7?
Q47:
Stage-it bids for two contracts, A and B. The probability that it will obtain contract A is 0.3, but 0.5 that it will obtain contract B. What is the probability that it will obtain either contract A or contract B?
1. Stage-it usually recruits 25 management trainees per annum. In 2012, 140 applications were received and of these: 78 had previous work experience; 43 had passed a vocational exam; 21 had both work experience and had passed a vocational exam (and had been included in the above figures).
(a) Use a Venn diagram to illustrate this situation.
(b) What is the probability that an applicant selected at random by Stage-it had previous work experience or had passed a vocational exam?
2. Can you suggest any situations in which a Venn diagram might be useful for Stage-it in its decision making?
Q48:
Stage-it has organised an event that involves five separate companies. The probability of any one company failing to complete its task is estimated at 0.03. What is the probability of all five companies successfully completing their designated tasks (i.e. of none failing to complete their task)?
Q49:
Stage-it requires floral decorations in a major event it is organising and has ordered seeds in good time to produce the blue flowers it requires. In a given batch of seeds, the probability of a seed germinating is 0.95. The probability of a blue flower coming from any one of the germinating seeds is 0.4. What is the probability that any one seed will result in a blue flower?