Respuesta :
Answer: 70
Step-by-step explanation:
Given that :
Uniform range of distribution = 50 to 100
50 ≤ x ≤ 100
Difference between both values = 100 - 50 = 50
Range / difference = computer generated value
(Weekly demand - lower limit) / difference = computer generated value
(Weekly demand - 50) / 50 = 0.4
Weekly demand - 50 = 20
Weekly demand = 20 + 50
Weekly demand = 70
The weekly demand if the corresponding computer-generated value is 0.4 is given by: Option B: 70
What is the property of a uniformly distributed random variable?
A uniformly distributed random variable's probability is distributed uniformly in the interval in which it is defined. Thus, if X ranges from a to b, and pertains uniform distribution, then its probability density function is given by;
[tex]f(x) = \dfrac{1}{b-a}; a < x < b\\\\f(x) = 0; x < a , b < x[/tex]
For the given case, the weekly demand(let it be tracked by random variable X) is in range 50 to 100.
The computer generated value shows:
[tex]\text{Computer generated value} = \dfrac{\text{Weekly demand} - \text{Lower limit}}{\text{difference between upper and lower limit}}[/tex]
(computer generated value is showing in range 0 to 1, the part occupied by the weekly value from starting, here as it is 0.4, so it means out of 50 values, it is 0.4 = 40% of (100 -50) = 20 (from start which is 50, thus, 50 + 20 = 70) )
As we've got:
- Computer generated value = 0.4
- Lower limit = 50,
- Difference between upper and lower limit = 100 - 50 = 50,
Thus, the weekly demand is obtained as:
[tex]0.4 = \dfrac{\text{Weekly demand} - 50}{50}\\\\\text{Weekly demand} = 0.4 \times 50 + 50 = 70[/tex]
Thus, the weekly demand if the corresponding computer-generated value is 0.4 is given by: Option B: 70
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