Quantitative

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First we need to calculate the expected value of revenues and then subtract it from investment costs:

E(X)==200000.7+00.3=14000[pic 9][pic 10][pic 11]

Profit= revenue-investment=14000-10000=4000>0

Therefore, it is a good investment.

- A company makes electronic gadgets. One out of every 60 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $5 profit on the sale of any working gadget, but suffers a loss of $100 for every faulty gadget because they have to repair the unit. Check whether the company can expect a profit in the long term

Probability of faulty=1/60; Probability of working gadgets=59/60;

Expected profit for each gadget: E(X)=(59/60)5-(1/60)100=3.25>0[pic 12][pic 13]

Hence the company can expect a profit in the long term.

- Intelligence quotients (IQs) measured on the Stanford Revision of the Binet-Simon Intelligence Scale are normally distributed with a mean of 100 and a standard deviation of 16. Determine the percentage of people who have IQs between 115 and 140.

=100; ;[pic 14][pic 15]

First transfer to standard normal distribution

= =0.9375; ==2.5;[pic 16][pic 17][pic 18][pic 19]

Then look into the table and find the related area:

[pic 20]

- As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. Determine the percentage of finishers with times between 50 and 70 minutes. (b) Determine the percentage of finishers with times less than 75 minutes.

µ=61, σ=9

- P(50

=(50-61)/9=-1.22[pic 21]

=(70-61)/9=1[pic 22]

Then look into the table and find the related area:

P(-1.22

- P(X

Z=(75-61)/9=1.56

P(z)=0.4406+0.5=0.9406=94.06%[pic 23]