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Allisa [31]
3 years ago
12

The random variable X is exponentially distributed, where X represents the waiting time to be seated at a restaurant during the

evening. If X has an average value of 19 minutes, what is the probability that the wait time is greater than 14 minutes
Mathematics
1 answer:
erastova [34]3 years ago
7 0

Answer:

The probability that the wait time is greater than 14 minutes  is 0.4786.

Step-by-step explanation:

The random variable <em>X</em> is defined as the waiting time to be seated at a restaurant during the evening.

The average waiting time is, <em>β</em> = 19 minutes.

The random variable <em>X</em> follows an Exponential distribution with parameter \lambda=\frac{1}{\beta}=\frac{1}{19}.

The probability distribution function of <em>X</em> is:

f(x)=\lambda e^{-\lambda x};\ x=0,1,2,3...

Compute the value of the event (<em>X</em> > 14) as follows:

P(X>14)=\int\limits^{\infty}_{14} {\lambda e^{-\lambda x}} \, dx=\lambda \int\limits^{\infty}_{14} {e^{-\lambda x}} \, dx\\=\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{14}=e^{-\frac{1}{19} \times14}-0\\=0.4786

Thus, the probability that the wait time is greater than 14 minutes  is 0.4786.

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We know that

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A coffee shop sells five different flavors of coffee. They want to compare how much of each is sold on Saturday morning. Which g
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Answer:

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Step-by-step explanation:

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pochemuha

Answer:

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Step-by-step explanation:


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Find the outlier in the data: 32, 40, 34, 31, 20, 36, 40, 31. How does the outlier affect the mean?
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Quiz 3
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Complete question :

The data below represents the number of customers at each Slurpee Sam's Spaghetti Shop. 24, 25, 29, 30, 31, 31, 32, 34, 34. Which box plot correctly summarizes the data?

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Step-by-step explanation:

BOX plots provide information about :

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Given the dataset :

24, 25, 29, 30, 31, 31, 32, 34, 34

Minimum value = 24 (Lowest value in the dataset)

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Second quartile ; median (Q2) = 1/2(n+1)th term

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First dot = minimum value

Last dot = maximum value

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4 0
2 years ago
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