Assume Project A has an expected value of $27,000 and a standard deviation () of

Question

Assume Project A has an expected value of $27,000 and a standard deviation () of $5,400.

a. What is the probability that the outcome will be between $24,300 and $29,700? (Round your answer to 4 decimal places.)
  

b. What is the probability that the outcome will be between $16,200 and $37,800? (Round your answer to 4 decimal places.)
  

c. What is the probability that the outcome will be at least $16,200? (Round your answer to 4 decimal places.)
  

d. What is the probability that the outcome will be less than $34,610? (Round your answer to 4 decimal places.)
  

e. What is the probability that the outcome will be less than $21,600 or greater than $29,700? (Round your answer to 4 decimal places.)
  

Number of 's
From Expected
Value + or – + and – .50 .1915 .3830 1.00 .3413 .6826 1.41 .4207 .8414 1.50 .4332 .8664 2.00 .4772 .9544

Explanation / Answer

a.) Expected Value of Project A=$27,000

Standard Deviation, =$5400

Expected Range Lower Bound =$24,300 i.e $27,000 - 0.50

Expected Range Upper Bound =$29,700 i.e $27,000 + 0.50

Referring the above table, probability for this scenario =38.30%

b.) Expected Value of Project A=$27,000

Standard Deviation, =$5400

Expected Range Lower Bound =$16,200 i.e $27,000 - 2.00

Expected Range Upper Bound =$37,800 i.e $27,000 + 2.00

Referring the above table, probability for this scenario =95.44%

c.) Expected Value of Project A=$27,000

Standard Deviation, =$5400

Expected Range Lower Bound =$16,200 i.e $27,000 - 2.00

Since, it is capped only at one end, we will use OR value from the table and add it in 0.50 to get the required area under the bell curve.

Referring the above table, probability for this scenario =0.50 + 0.4772 = 97.72%

d.) Expected Value of Project A=$27,000

Standard Deviation, =$5400

Expected Range Upper Bound =$34,610 i.e $27,000 + 1.41

Since, it is capped only at one end, we will use OR value from the table and add it in 0.50 to get the required area under the bell curve.

Referring the above table, probability for this scenario =0.50 + 0.4207 = 92.07%

e.) Expected Value of Project A=$27,000

Standard Deviation, =$5400

Expected Range Lower Bound =$21,600 i.e $27,000 - 1.00

Expected Range Upper Bound =$29,700 i.e $27,000 + 0.50

Since, we required areas outside the lower and upper bound which are not symmetrical with respect to the centre, we will use OR value from the table and will calculate the areas for both these cases separately.

Probability that outcome will be less than $21,600 = 0.50-0.3413 =15.87%

Probability that outcome will be more than $29,700 = 0.50-0.1915 =30.85%

Referring the above table, probability for this scenario =15.87 + 30.85 = 46.72%

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