The time (in minutes) between arrivals of customers to a post office isto be modelled by the Exponential distribution with mean 0.4.Part a)What is the probability that the time between consecutive customersis less than 15 seconds?Part b)Find the probability that the time between consecutive customers isbetween ten and fifteen seconds.Part c)Given that the time between consecutive customers arriving isgreater than ten seconds, what is the chance that it is greater thanfifteen seconds?

Answered: Image /qna-images/answer/a134b4d4-6360-433d-96ea-82aac75c2735.jpg

Answered: The time (in minutes) between arrivals…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Today, the waves are crashing onto the beach every 4.4 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.4 seconds. Round to 4 decimal places where possible. The probability that the wave will crash onto the beach between 1.2 and 2.1 seconds after the person arrives is P(1.2 < x < 2.1) = The probability that it will take longer than 3.28 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.28) = Suppose that the person has already been standing at the shoreline for 0.7 seconds without a wave crashing in. Find the probability that it will take between 3 and 3.7 seconds for the wave to crash onto the shoreline. 62% of the time a person will wait at least how long before the wave crashes in? seconds. Find the minimum for the upper quartile. seconds. Hint:
Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 2.64 days. A random sample of 81 shipments are selected and their shipping times are observed. Find the probability that the average shipping time is less than 2.28 days.
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The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)
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