#16 Rude Drivers: Tailgating About 35% of all drivers will tailgate before passing, thinkingthey can make the car in front of them go faster. Suppose that you are driving a considerabledistance on a two-lane highway and are passed by 12 vehicles.(a) Let r be the number of vehicles that tailgate before passing. Make a bar graph showingthe probability distribution of r for r = 0 through r = 12.(b) Compute the expected number (µ) of vehicles out of 12 that will tailgate.(c) Compute the standard deviation (ơ) of this distribution.

If an experiment has been happen for a success of an event is calculated using Bernoulli…

Answered: #16 Rude Drivers: Tailgating About 35%…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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On average, TV crash after 17,000 hours of continuous use. Although the time for the TV to crash is random, researchers have found that the duration until the computer crashes follows an exponential probability distribution. a. What is the probability that the TV will fail with a usage time of less than 17,000 hours?b. What is the probability that the TV will crash with a usage time of more than 17,000 hours?c. What is the probability that no TV will fail after more than 17,000 hours of use?d. What do you think about the results of points b and c above! What is the difference?
The number of x people entering the intensive care unit (ICU) at a particular hospital on any givenday has a Poisson probability distribution with mean equal to five persons per day. What is the probabilitythat the number of people entering the ICU on particular fay is less than equal to two?
As you walk into your econometrics exam, a friend bets you $10 that she will outscore you on the exam. Let ✗ be a random variable denoting your winnings. X can take the values 10, if you win teh bet, 0 if there is a score tie, or -10 if you lose. You know that the probability distribution for ✗ is denoted by f(x) and it depends on whether she studied for the exam or not. Let Y be the random variable that indicates if she studied, Y = 0 if she studied and Y = 1 if she did not study. The following table denotes the joint distribution of X and Y : Y=0 Y=1 f(x) X = -10 0.18 P1 P2 X = 0 0 P3 0.3 X = 10 P4 0.45 P5 f(y) P6 0.75 Probabilities P1, P2, P3, P4, P5, P6 are not displayed in the table. Answer the following items: (a) (b) (a) Compute the Probabilities P1, P2, P3, P4, P5, P6 of the table. (b) Compute the expectation E(X). Should you take the bet? (c) What is the probability distribution of your winnings if you know that she did not study, namely, P(X = −10|Y = 1), P(X = 0|Y = 1), P(X…
Just answer as many problem you desire
Roll two fair dice. Use the Poisson approximation to find the probability that you will rollat least one double (meaning both dice land on the same value) in 24 trials. How does this compare tothe exact value? Answer as if explaining to someone.
A company that sells binders decides to run a promotion on their 1-inch and 2-inch size binders. Theydiscount the 1-inch binders to $1 per binder and discount the 2-inch binders to $2 per binder. They limitsales to a quantity of 5 of each size of binder per customer. The probability distribution of “X = the numberof 1-inch binders purchased by a single customer during the promotion period” is given in the table below. X 1 2 3 4 5 P(X) 0.02 0.09 0.12 0.15 0.62 a) Compute the mean and standard deviation of X. b) The company’s cost of manufacturing a single 1-inch binder is $0.25. What is the expected profit (indollars) that the company will make, per customer, for 1-inch binder sales during the promotion? c) The mean and standard deviation of “Y = the number of 2-inch binders purchased by a singlecustomer” is 2.74 and 1.25, respectively. Assume that the number of 1-inch and 2-inch binderspurchased are independent random variables. What are the mean and standard deviation of the…
We Love Cocoa! sells two-pound boxes of assorted chocolates. Because of imperfections in their equipment, the actual weight of the box of chocolates has a continuous uniform distribution ranging from 31.8 to 32.6 ounces. What is the probability that a box weighs exactly 31 ounces?
Imagine that you are training to run a half-marathon and so every week you have 2 intense days, 3 light days, and 2 rest days. On your intense days you run 16 km, on your light days you run 5 km, and on your rest days you do not run. How would you model your miles run per day as a random variable? (Hint: probability distribution)
Bernoulli process: i.Draw the probability distributions (pdf) for X∼bin (8, p) (x) forp = 0.25, p = 0.5, p = 0.75, in each diagram.ii.What kind of effect has a higher value on the graph , compared to a lower value? iii.You should strike a coin8gonger. You win if there are precise4 or precise5 coins, but otherwise lose. You can choose between three different coins, medpn = P (coin) respectively p1 = 0.25, p2 = 0.5, andp3 = 0.75. Which of these coins gives you the highest probability of winning?
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
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