The probability that demand is greater than 1800 gallons over a 2 hour period is : 0.5
<u>Given data :</u>
Mean value of gasoline per hour = 875 gallons
Standard deviation = 55 gallons
<h3>Determine the probability of demand being greater than 1800 gallons over 2 hours </h3>
Demand for gas in 1 hour = X₁
Demand for gas in 2 hours = X₁ + X₂
Therefore ; ( X₁ + X₂) ~ N ( u₁+u₂, sd₁² + sd₂² )
In order to calculate probabilities for normals apply the equation below
Z = ( X- u ) / sd
where : u = 1800, sd = √ ( 55² + 55² ) = 77.78
using the z-table
P( Y > 1800) = P( Z > ( 1800 - 1800 ) / 77.78)
= P( Z>0 ) = 0.5
Hence we can conclude that The probability that demand is greater than 1800 gallons over a 2 hour period is : 0.5.
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Answer:
Average rate of return= 10.17
%
Geometric return = 9.23%
Explanation:
<em>Geometric average return</em>
This is compounded annual rate of return which is used to measure the performance of an asset over a certain number of years. It helps to measure the return generated by an investment taking into account the volatility .
Unlike the arithmetic average the geometric average gives an idea of the real rate taking into account of volatility
The formula below
Geometric Return =(1+r1) (1+r2) ...... (1+rn)^1/n
Geometric Average return =
(1.12× 1.19× 1.21× 0.88× 1.26× 0.95)^(1/6) - 1 =0.09233168
Geometric return =0.0923
× 100= 9.23%
Geometric return = 9.23%
Average rate of return
<em>The average return is the sum of the returns over the years dividend by the Numbers of returns</em>
Average return = sum of return / No of returns
(12% + 19% + 21% + (12%) + 26% + (5%))/6 =10.17
%
Average rate of return= 10.17
%
Geometric return = 9.23%
