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# Break-even Analysis & Probability

Please assist if is possible with a neat step by step calculations . Thanks!

1)
a) In a business environment, the fixed cost is \$2,000.00 and the variable cost is \$20.00. As we know, the brake even volume v and the brake-even price p are related by formula:
V=2000/P-20
The formula describe the relationship between the above two quantities. Solve for P to obtain an expression for the brake-even price in terms of the brake-even volume.

b) In excel, construct two columns; one for the values of v (starting with 10, ending with 200, and increasing in increments of 5 each time)
The other column will contain the corresponding p values according to the formula obtained above. Then construct a scatter line plot of the pair (v, p). Comment on the shape and the behavior of the graph regarding the relationship between v and p.
The following is only a portion of the table. The values shown are accurate.
v p
10 220.00
15 153.33
20 120.00
25 100.00
Now suppose the business mentioned above has aimed to finalize a net profit of \$1000.00 start with the formula for the profit
Z=(P-Cv)v-Cf; or 1000=(P-20)v-2000
again solve for P to obtain an expression for the price in terms of the volume v.
2)
According to a recent survey, one out of three divorce results as a consequence of spousal abuse. A random sample of 15 divorce cases is chosen.
a) what is the probability that 6 in the sample have been consequences of spousal abuse?
b) ) what is the probability that 8 in the sample have been consequences of spousal abuse?
c) what is the probability that 10 in the sample have been consequences of spousal abuse?
d) what is the probability that 7 but less than 12 divorces have been consequences of spousal abuse?
e)construct a tabular and graphical probability distribution for the number of divorces among 15 which has been a consequence of spousal abuse.

f) construct a tabular and graphical cumulative probability distribution for the number of divorces among 15 which has been a consequence of spousal abuse
g) on the average hoe many divorces among 15 do you expect to be the consequence of spousal abuse? (please show calculation)

3) please do in excel : the lifetime of a brand of television has a normal distribution with a mean of 7 years and a standard deviation of 1.5 years.

a) What percentage of these television last more than 8 years?
b) What percentage of these televisions last between 5 and 9 years?
c) Find a lifetime such that only 3% of these TVs will last more than this life time.
d) The quality control manager has decided to choose a warranty period that only at most 1% of the time the TVĂ˘??s are covered by the warranty, What should be the warranty period?
3) The buyer of a 10 acre-forestland will buy the land if at least 10% of its trees are 40 feet or taller. The seller has disclosed that the distribution on the trees is almost normal with a mean of 32 and the standard deviation of 3 feet. Will the buyer buy the land?

4) According to a recent health study, 25% of adult males have circulation problem. Males who have circulation problems are twice as likely to be smokers as those who do not have a circulation problem. What percentage of male smokers have circulation problems? What percentage of nonsmokers have circulation problem?

#### Solution Summary

The solution provides step by step method for the calculation of break-even analysis and probability using binomial and normal distributions. Formula for the calculation and Interpretations of the results are also included.

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