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stealth61 [152]
3 years ago
12

A new diner opens on our street. It will be open 24 hours a day, seven days a week. It is assumed that the inter-arrival times b

etween customers will be i.i.d.(independent and identically distributed) exponential with mean 10 minutes. Approximate the probability that the 120th customer will arrive after the first 21 hours of operation. Enter your answer to 4 decimal places.
Mathematics
1 answer:
klio [65]3 years ago
6 0

Answer:

0.2912

Step-by-step explanation:

Given that:

Duration new diner will be opened is24 hours a day. It is assumed that the Inter arrival times between customers will be i.i.d exponential with mean 10 minutes

A collection of random variables is independent and identically distributed (i.i.d) if each random variable has the same probability distribution as the others and all are mutually independent.

Expected time for 120 customers = 120 ×10 = 1200 minutes

Standard deviation = \sqrt{120*10^{2} } = 109.5445

P(It takes more than 21 hours) = 21 × 60 =1260 minutes

Probability = P(X > 1260) = P(Z > ((1260-1200)109.5445)

P(X > 1260) = P(Z > (60/109.5445)

P(X > 1260) = P(Z>0.55)

P(X > 1260) = 1 - P(Z<0.55) = 1 - 0.7088 = 0.2912

The probability that the 120th customer will arrive after the first 21 hours of operation is 0.2912

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Answer:

Step-by-step explanation:

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The width of a rectangular prism is six times its length. The height is five times its length. If its length is m units, what is
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Answer:

30m^3 cubic units.

Step-by-step explanation:

Let m represent length of the rectangular prism.

We have been given that the width of a rectangular prism is six times its length, so width of the prism would be 6m.

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We know that volume of rectangular prism is height times width times length.

\text{Volume of rectangular prism}=lwh

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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radius is always half the length of its diameter. For example, if the diameter is 4 cm, the radius equals 4 cm ÷ 2 = 2 cm.

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