The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m. a. What is the probability that there will be exactly 8 cracks in a 500 m length of pavement b. What is the probability that there will be no cracks in a 100 m length pavement c. Let ? be the distance in meters between two successive cracks. What is the probability density function of ? d. What is the probability that the distance between two successive cracks will be more than 50 m

The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m. a. What is the probability that there will be exactly 8 cracks in a 500 m length of pavement b. What is the probability that there will be no cracks in a 100 m length pavement c. Let ? be the distance in meters between two successive cracks. What is the probability density function of ? d. What is the probability that the distance between two successive cracks will be more than 50 m

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...

See similar textbooks

Related questions

Q: The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5.) Draw a density curve and use the calculator to determine the probability. Write the calculator…

A: According to the Bartleby guidelines expert solve only one question and rest can be reposted.

Q: ccording to a study done by UCB students, the height for Asian adult males is normally distributed…

A: Given : The height for Asian adult males is normally distributed with an average of 64 inches and a…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: Reviewing information, X : Distance of flyball in feet μ=268 feetσ=37 feet

Q: Today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives…

Q: According to a study done by UCB students, the height for Martian adult males is normally…

A: a. The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the…

Q: Let H be the discrete r.v. that represents the number of heads obtained when a fair coin is flipped…

A: Given information- We have given that a fair coin is flipped for one time. Let, H be the discrete…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: a) The distribution of X ~ N(267, 1296) is and it is identified below: Let X be the distance of fly…

Q: mean of 256 feet and a standard deviation of 38 feet. Let X be the distance in feet for a fly ball.

A: Let X be the random variable such that the distance of fly balls hit to the outfield (in baseball).…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: Step 1:Given the information:The mean distance of fly balls, μ=267 feetThe standard deviation, σ=44…

Q: The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 70 mph and…

A: Standard normal distribution:The standard normal distribution is a special case of normal…

Q: The graph shows the probability density function for a car brand that has a mean fuel efficiency of…

A: Given: Meanμ=26standard deviation(σ)=2.4

Q: The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70…

A: (a) X ~ N(70, 14) (b) P(X>85) = P(Z>85-7314) = P(Z>0.8571)…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 71 mph…

A: Since this is multiple choice question , first two parts are answered step by step. Please repost…

Q: Suppose the time it takes my daugther, Lizzie, to eat an apple is uniformly distributed between 6…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 79 mph and…

A: From provided information; X be the speed for a randomly selected car. Speed at which cars go on…

Q: Assume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per…

A: Draw the normal curve and shade the area to the left of z=0.24. Refer to Standard normal…

Q: Assume that females have pulse rates that are normally distributed with a mean of u = 76.0 beats per…

A: Given data: Mean = 76 Standard deviation = 12.5

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: Given μ=267σ=42 a) The distribution of X is N(267, 42). b) The probability that a randomly hit fly…

Q: The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62…

A: Note: Hi there! Thank you for posting the questions. As there are multiple sub parts, according to…

Q: Assume that females have pulse rates that are normally distributed with a mean of u= 72.0 beats per…

Q: The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 4…

A: From the given information we find the solution.

Q: The average number of miles (in thousands) that a car's tire will function before needing…

A: Given data, μ=71σ=19n=18we have to complete the distribution and their probabilities

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and…

Q: A bus comes by every 13 minutes. The times from when a person arives at the busstop until the bus…

A: As per guidelines expert have to answer first question three subparts only dear student please…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 72 mph and…

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want a…

Q: The mean number of bacteria per millimeter of a liquid is known to be 4. Assuming that the number of…

A: We have, The mean number of bacteria per millimeter of a liquid is known to be 4. Assuming that the…

Q: a. What is the distribution of X? X ~ N(,) b. If one car is randomly chosen, find the probability…

A: [NOTE : As per the rules only the first three sub-parts are solved.] Given that, The speed at…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 74 mph and…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: a. The distribution of x is X~N(263,43)μ=263σ=43

Q: The number of tourists arriving in a certain tourist destination is assumed to follow a Poisson…

A: Givendaily mean rate of 500 λ=500x~Poisson(λ=500)P(X=x)=e-λ×λxx! ; x≥0

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 70 mph and…

A: Since, you have you have posted a question with multiple subparts we will solve first three subparts…

Q: In a plastic manufacturing company, the melting temperatures of PVC items are assumed to follow a…

A: Given that each package has average melting temperature is 180 C and the standard deviation is 20C.…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: Standard normal distribution:The standard normal distribution is a special case of normal…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: The random variable distance for a fly ball follows normal distribution. We have to find the…

Q: Suppose that 2 balls are randomly selected from an urn containing 3 red, 4 blue, and 5 white balls.…

A: Given: Red balls: R1, R2, R3 Blue balls: B1, B2, B3, B4 White balls: W1, W2, W3, W4, W5 X: Number of…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and…

Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: The reaction time X (in minutes) of a chemical process follows a uniform probability distribution…

A: The reaction time X (in minutes) of a chemical process follows a uniform probability distribution…

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m.

a. What is the probability that there will be exactly 8 cracks in a 500 m length of pavement

b. What is the probability that there will be no cracks in a 100 m length pavement

c. Let ? be the distance in meters between two successive cracks. What is the probability density function of ?

d. What is the probability that the distance between two successive cracks will be more than 50 m

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile. 1. Determine the probability mass function of the number of cracks (X) in 5 miles of highway. 2. Calculate the mean and variance of X
Suppose that the speed at which cars go on the freeway is normally distributed with mean 75 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,) b. If one car is randomly chosen, find the probability that it is traveling more than 72 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 76 and 80 mph. d. 78% of all cars travel at least how fast on the freeway? mph.
The length of eels (in cm) in a river may be assumed to be normally distributed with a mean of µ = 42 and a standard deviation of o = 6. An angler catches an eel from a river. Let: X = the length (in cm) of an eel a) If the normal length of eels is between 30 cm and 45 cm, what percentage of eels fall within this normal range? Round your answer to 2 decimal places. b) What is the probability that an eel is at least 51 cmin length? Round your answer to 4 decimal places. c) The middle 50% of the lengths (in cm) of the eels are between and Round your answers to 2 decimal places d) Due to the symmetry of the normal distribution we know that DIV 20 - DIV -
The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N b. Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected person at the hot springs stays longer then 82 minutes. c. The park service is considering offering a discount for the 5% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.
Today, the waves are crashing onto the beach every 4.2 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.2 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is C. The probability that it will take longer than 2.14 seconds for the wave to crash onto the beach after the person arrives is P(x > 2.14) = %3D
A randomly selected group of 560 students are assumed to have heights distributed normally with meanµ = 166 cm and standard deviation σ = 30 cm. Suppose a student is chosen randomly from this group. Finda. the probability that this student’s height is between 170 cm and 182 cm.b. the probability that this student’s height is bigger than 175 cm.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 268 feet and a standard deviation of 45 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 338 feet. Round to 4 decimal places. c. Find the 90th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feet
Assume that females have pulse rates that are normally distributed with a mean of u=75,0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. ne a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. ent The probability is (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? O A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. O B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size. OC. Since the distribution is of sample means, not individuals,…
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 17 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected person at the hot springs stays longer then 70 minutes. c. The park service is considering offering a discount for the 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.Q1: minutesQ3: minutesIQR: minutes
The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X~ N( b. Find the probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.
Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(Correct,Correct) b. If one car is randomly chosen, find the probability that it is traveling more than 72 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 73 and 78 mph. d. 88% of all cars travel at least how fast on the freeway? mph.