these cards are put int a bag. One card is chosen at random. (1,2,3,4,5,6,7,8,9,10) a.) what is the probability of choosing the
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It can be expected about 36.79% of chance that repair time exceeds
The probability that a repair time exceeds 15 hours is 0.3679
What is the exponential distribution?
It explains about the time between events or the distance between two random events is termed the exponential distribution. Here, the occurrence of the events is continuous and also independent. Moreover, the average rate is constant.
The cumulative distribution function of T is obtained below:
From the information given, let the random variable T be the required time to repair a machine follows exponential distribution with parameter λ
with mean. 1/2 hours
That is, E(x) = 1/2 hours.
The parameter of the random variable T is,
E(x) = 1/λ
λ = 1/E(x)
= 1/(1/2)
= 2
The probability density function of T is,
The cumulative density function of T is,
FT(t) = P(T <= t)
The CDF of T is,
P(T <= t) 0 <= T <= ∞
= 0 otherwise
to obtain the probability that a repair time exceeds
1/2 hours.
(a) The probability that a repair time exceeds 1/2 hours.
From the given information, the CDF of T is,
P(T <= t) 0 <= T <= ∞
= 0 otherwise
The required probability is,
P(T <= 1/2) = 1 - P(T <= 1/2)
= 1 - [ ]
= 0.3679
om total probability. It can be expected about 36.79% of chance that repair time exceeds
P(X => x) = 1 - P(X < x)
to obtain the probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours.
(b), The probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours is obtained below:
From the given information, the CDF of T is,
P(T <= t) 0 <= T <= ∞
= 0 otherwise
The required probability is,
P = P(T => 12.5∩T>12) / P(T>12)
= 0.3679
The probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours is obtained by dividing the
P = P(T => 12.5∩T>12) / P(T>12)
with
P(T>12).
It can be expected about 36.79% of chance that a repair takes at least 12.5 hours given that its duration exceeds 12 hours.
Hence, It can be expected about 36.79% of chance that repair time exceeds,
The probability that a repair time exceeds 15 hours is 0.3679
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Answer:
1092
Step-by-step explanation:
We have been given that the number of bacteria in the colony t minutes after the initial count modeled by the function . We are asked to find the average rate of change in the number of bacteria over the first 6 minutes of the experiment.
We will use average rate of change formula to solve our given problem.
Upon substituting our given values, we will get:
Therefore, the average rate of change in the number of bacteria is 1092 bacteria per minute.