The number of calls received at a 24-hour service desk follows a Poisson distribution that has a standard deviationof 0.8 per minute.a) Find the probability that the service desk will receive more than 3 calls in the next 5 minutes.b) Find the probability that the time between the last call and the next call will be between 1 to 4 minutes.c) Let X be the time until he receives 3rd call. Find the P(X < 5) and the moment generation function of X.

Given that the number of calls received at a 24-hour service desk follows a Poisson distribution…

Answered: The number of calls received at a…

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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A bus heading to university is always scheduled to arrive at a certain bus stop at 7:30am. The difference between the actual arrival time and 7:30am is normally distributed with mean 0 and standard deviation of 2 minutes.A student who always has a class at 8am decided to be at the bus stop at 7:28am in order to try to guarantee catching this bus. What is the probability that the student will catch the bus on any particular day?Probability = What is the probability that the student will catch the bus at least 4 times out of 5 days?Probability =
The mean incubation time for a type of fertilized egg kept at a certain temperature is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days. Complete parts (a) through (e) below. b. Find and interpret the probability that a randomly selected fertilized egg hatches in less than 20 days. c. Find and interpret the probability that a randomly selected fertilized egg takes over 24 days to hatch. d. Find and interpret the probability that a randomly selected fertilized egg hatches between 18 and 22 days. e. Would it be unusual for an egg to hatch in less than 16 days? Why? The probability of an egg hatching in less than 16 days is __ so it would not or would be unusual, since the probability is greater or less than 0.05.
E The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
The population of college students using “normal shoes” is able to complete a particular racecourse in an average of 250 seconds. The standard deviation for this population is 20 seconds and the population is normally distributed. A random sample of 28 college students is given a special pair of new shoes and asked to run the course. The average “race time” for this group is 243 seconds. assume now that the designer of the shoes states that his shoes should improve the times of the user (less time to finish the race). State the hypotheses involved. determine if the hypothesis test is one tailed or two tailed Give the Z scores associated with cut-off points for .01, .05, and .10 (1%, 5%, and 10% respectively). Calculate the Z score for this problem. Based on a cut-off point or alpha level of .05 (5%), what decision would you make about your hypotheses? Explain this decision. Make conclusions regarding the specifics of this study.
assume that X is normally distributed with a mean 150 and standard deviation of 40. find the probability that (A) x is less then 145 and (B) x is grater then 170
Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of e- 12.5 beats per minute. Complete parts (e) through (c) below a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute The probability is 5048 (Round to four decimal places as needed.) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is (Round to four decimal places as needed.)
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of 36 and a standard deviation of 10. Suppose that one individual is chosen at random. Find the following (round to 4 decimal places) a) Find the probability that the percent of fat calories a person consumes is more than 40. b) Find the probability that the percent of fat calories a person consumes is less than 35. c) Find the maximum number for the lower quartile of percent of fat calories. d) The middle 70% of the percent of fat calories are from 4 to
22
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 265 feet and a standard deviation of 40 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 264 feet. Round to 4 decimal places.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 275 feet and a standard deviation of 35 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly hit fly ball travels less than 265 feet. Round to 4 decimal places.
The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are between 200 and 400 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places.
Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in?…

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