Home Improvement Contractor - Licensed Contractors
Introductory Probability and Statistics HELP!!!?
Problem 1 A building contractor has sent in bids for three jobs. If the contractor obtains these jobs, they will yield respective profits of $20,000, $25,000 and $40,000. On the other hand, for each job that the contractor does not win, due to time and money already spent on making the bid he will incur a loss (interpreted as a negative profit) of $2,000. If the probabilities that the contractor will get these jobs are, respectively, 0.3, 0.6, and 0.2, what is the expected total profit? Problem 2 A saleswoman has a 60% chance of making a sale each time she visits a computer store. She visits 3 stores each month. Assume that the outcomes of successive visits are independent. 1. What is the probability she makes no sales next month? 2. What is the probability she makes two sales next month? 3. What is the probability that she makes at least one sale in each of the next three months? Problem 4 Jet pilots and astronauts are often exposed to high accelerations, which they must be able to bear without collapsing. In tests it was found that their blackout thresholds are normally distributed with mean 4.5g and standard deviation 0.7g (1g is the unit of gravitational acceleration). Only those pilots whose thresholds are in the top 25% are allowed to apply to become astronauts. What is the lowest blackout threshold a pilot must have to become an astronaut?
Public Comments
- I assume the profits net out the $2,000 cost: (.3)$20,000 + (.6)$25,000 + (.2)$40,000 + (.7)(-$2000) + (.4)(-$2000) + (.8)($-2000) = Expected value No Sales: (.4) (.4) (.4) Two Sales: 3C2 (.6)^2 (.4)^1 One Sale or more sales in a month: s = 1 - (No Sales) Probability of at least one sale in each month assuming each month is independent: s^3 z = .68 for an area of .25 sd = .7 cutoff = 4.5 + .7(.68)
- Oki Koki.. Problem One: Just reading this question makes you dizzy. Pick out all the numbers you need, and attach them to the respective probabilities. So we've got the first job: 20,000 if he gets it - 0.3 chance he gets it -2000 if he doesnt - 0.7 he doesnt. we time the probabilities by the respective amounts to be lost or gained. eg, 20,000 x 0.3 = 6000 -2000 x 0.7 = -1400 and then add up those amounts: = 6000 + -1400 = 6000 - 1400 = 4600 if you do this for all of the jobs, and add up the amounts, you will get the total profit, which should equal $25200. Just remember that the $2000's are negative and you should be fine =] Problem Two: 1. No sales. So she goes to three shops, 60% chance of buying each time. 40% chance she doesnt buy. so all you do here is: 40% x 40% x 40% =0.064 2.two sales Theres three ways around this. Her sale pattern could be: SALE, no sale SALE SALE, SALE, no sale no sale, SALE, SALE. so her probabilities look like this: 0.6 x 0.4 x 0.6 0.4 x 0.6 x 0.6 0.6 x 0.6 x 0.4 add these up and you get 0.432. 3. One sale in each of three months again, it could go SNN = 0.6 x 0.4 x 0.4 NSN = 0.4 x 0.6 x 0.4 NNS = 0.4 x0.4 x 0.6 add these up, gives = 0.288 now this needs to happen three times, so we times it by itself three times = 0.02 Problem 4. Normal distribution, lovely =] You need to draw a diagram really, but I'll try and explain. right, we've been given the mean & sd, X values.. We know that the top 25% can be astronauts - this is a z value. if you draw a diagram, and shade the top 25%, it'll make sense that the threshold X value we're looking for is in z terms 75%. P(z > 0.75) so we consult our normal distribution table, and look for 0.75, which gives us the value 0.7734. Howver, we want to know bigger than .75 - bigger than a positive, which means the probablility is 1 - 0.7734 = 0.2266. so to find x, we use the formula z = (x - mean) / standard deviation 0.2266 = (x - 4.5) / 0.7 0.2266 x 0.7 = x - 4.5 0.15862 + 4.5 = x x = 4.65862 x = 4.7g which means that pilots must withstand more than 4.7g's to become an astronaut. Hope this helps =]
