Answer:
0.4966
Explanation:
For an exponentially distributed probability;
X = 700
The mean m = 1/h
Mean m = 1000
h =1/1000 = 0.001
For,
The probability that the lifetime is greater than or equal to 700 days
P(x>700) = integral( upper limit infinite, lower limit 700){h*exp(-hx)}dx
P(x>700) = 0- (-exp(-h*700)) = exp(-0.001*700) = exp(-0.7) = 0.4966
Therefore the probability that the lifetime is greater than or equal to 700 days is 0.4966
The probability that the lifetime is greater than or equal to 700 days is 0.4966
The exponential distribution in probability theory and statistics is the distribution function of the time among events in a Poisson point distribution process.
From the given information, for an exponentially distributed probability;
The mean (=1000) of the distribution = [tex]\mathbf{\dfrac{1}{\lambda }}[/tex]
where;
Thus; the probability that the lifetime is ≥ 700 days is:
[tex]\mathbf{P(X \geq 700) = 0 - (e^{(-\lambda \times 700)})}[/tex]
[tex]\mathbf{P(X \geq 700) = 0 - (e^{(-0.001 \times 700)})}[/tex]
[tex]\mathbf{P(X \geq 700) = 0 - (e^{(-0.7)})}[/tex]
P(X ≥ 700) = 0.4966
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