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sammy [17]
3 years ago
7

The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a

mean of 4 minutes. a. Find the value of λ. b. What is the probability that a person waits for less than 3 minutes?
Mathematics
1 answer:
Leya [2.2K]3 years ago
3 0

Answer:

a) 0.25

b) 52.76% probability that a person waits for less than 3 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \lambda e^{-\lambda x}

In which \lambda = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

In this question:

m = 4

a. Find the value of λ.

\lambda = \frac{1}{m} = \frac{1}{4} = 0.25

b. What is the probability that a person waits for less than 3 minutes?

P(X \leq 3) = 1 - e^{-0.25*3} = 0.5276

52.76% probability that a person waits for less than 3 minutes

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Step-by-step explanation:

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If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

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Hope this helps!! :)

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(4)² ÷ 4

16 ÷ 4

= 4 (PED)

8 0
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