Question

A venture capital firm is evaluating the performance of a possible high tech investment. Bill Buce, a senior partner, has suggested using a continuous uniform distribution to model net income. Bill believes the net income for year one will vary between 5.59 and 14.7 (in millions).

What net income should Bill forecast if he wants to be 84% sure net income will not exceed his forecast?

Forecasted net income =  (Enter your answer to 2 decimal places.)

Answer 1

Solution :

Given that,

a = 5.59

b = 14.7

PERCENTILE

= a + (b - a)p

= 5.59 + (14.7 - 5.59) * 0.84

= 13.24

Forecasted net income = 13.24 ( in millions)

Answer 2

Given that the net income follows a continuous uniform distribution between 5.59 and 14.7 (in millions), we can use the properties of the uniform distribution to find the required forecast.

Solution:

1. Identify the parameters of the uniform distribution:

• Lower bound ($a$) = 5.59

• Upper bound ($b$) = 14.7

• 
  

2. Understand the cumulative distribution function (CDF) for a uniform distribution:
   The probability that the net income $X$ is less than or equal to $x$ is given by:

   $$P(X\le x)=\frac{x-a}{b-a}$$

   We want this probability to be 84%, or 0.84.

3. 
   

4. Set up the equation and solve for $x$:

   $$\frac{x-5.59}{14.7-5.59}=0.84$$

   Calculate the denominator:

   $$14.7-5.59=9.11$$

   Now, solve for $x$$x$:

   $$x-5.59=0.84\times 9.11$$$$x-5.59=7.6524$$$$x=5.59+7.6524$$$$x=13.2424$$

5. 
   

Answer:

The forecasted net income should be 13.24 (in millions) to be 84% sure that net income will not exceed this value