question archive When returns from a project can be assumed to be normally distributed (represented by a symmetrical, bell?shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations
When returns from a project can be assumed to be normally distributed (represented by a symmetrical, bell?shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations
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When returns from a project can be assumed to be normally distributed (represented by a symmetrical, bell?shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations. For example, 68.26 percent of the distribution will fall within one standard deviation of the expected value (D ± 1σ). Similarly, 95.44 percent will fall within two standard deviations (D ± 2σ), and so on. An abbreviated table of areas under the normal curve is shown here. (Round the final answers to 2 decimal places.)
Number of σs from Expected
Value + or - + and -
0.50 0.1915 0.3830
1.00 0.3413 0.6826
1.11 0.3665 0.7330
1.50 0.4332 0.8664
2.00 0.4772 0.9544
Assume Project A has an expected value of $39,000 and a standard deviation (σ) of $7,800.
d. What is the probability the outcome will be less than $44,380?
Probability ..........................................%
e. What is the probability the outcome will be less than $35,100 or greater than $46,800?
Probability ....................................%
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d.) 77.07%
e.) 53.28%
Step-by-step explanation
d.) Probability of less than particular range can be derived in excel using inbuilt function 'NORM.DIST'
=NORM.DIST(44780,39000,7800,TRUE)
=77.07%
e.) Here we want to find the probability for the range of $35,100 and $46,800
We can calculate this using two method:
1.) $39,000 - $35,100 = $3,900 Which is 0.5 standard deviation from mean (3900/7800 = 0.5)
$46,800 - $39,000 = $7,800 which is 1 standard deviation from mean.
So, 0.5 times standard deviation in lower side and 1 standard deviation in upper side: = 0.1915 + 0.3413 = 0.5328
2.) Probability of value less than $46,800 - Probability of Value less than $35,100
=NORM.DIST(46800,39000,7800,TRUE) - =NORM.DIST(35100,39000,7800,TRUE)
= 0.8413 - 0.3085 = 0.5328
