statistics word problem.????

Question

before negotiating a longterm construction contract, building contractors must carefully estimate the total cost of completing the project. A guy proposed a model for the total cost of a longterm contract based on the normal distribution. For one particular construction contract the guy assumed total cost x to be normally distributed with mean $850,000 and standard deviation $170,000. The revenue R promissed to the contractor is $1,000,000.
a). the contractor will be profitable if revenue exceeds total cost. what is the probability that the contract will be profitable to the contractor?
b). what is the probability that the project will result in a loss for the contractor?
c). suppose the contractor has the opportunity to renegotiate the contract. What value of R should the contractor strive for in order to have a .99 probability of making profit?

Answer 1

a) Probability that this will be profitable for the contractor is .7224

b) .2776

c) $1,246,100

Answer 2

a) first find the zscore, use 999,999 since it is the highest the cost can be to be profitable. z=999,999-850,000/170,000 gives you a zscore of .8823. Use normalcdf(-99,.8823) gives you .8112. This means there is an 81.12% chance of making a profit.
b) simply take that amount and subtract it from 1
1-.8112=.1888, or 18.88%. This may be slightly off since we should have used 1,000,001 instead of 999,999 for the zscore.
c)use invNorm(.005), which gives you the zscore of 99% of one tail since it is top 99, not what falls into 99% of the amount, so you only use one side, = a zscore of 2.576

now do zscore formula: 2.576= x - 850,000/170,000
which comes out to roughly $1,287,920
Hope this helps

Answer 3

a. 0.8112
Cumulative Distribution Function
x...........................P( X <= x )
1000000....................0.8112

b. 0.1888

c. 1.25M
Inverse Cumulative Distribution Function
P( X <= x )...................x
0.9900...............1.25E+06