51. A local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it isrepaired the same day. Assume that breakdowns of individual cabs occur completely atrandom at a rate of two per year.a. What is the probability that any particular cab will run for a full year withoutsuffering a breakdown?b. What is the probability that the entire fleet will run for one month without abreakdown?c. On the average, how many breakdowns would the fleet expect in a typical three-month period?

Given Information Failure rate of an item chosen at random λ = 2

Answered: 51. A local cab company maintains a…

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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23. Precipitation In Akron, Ohio, the mean number of days in April with 0.01 inch or more of precipitation is 14. Find the probability that the number of days in April with 0.01 inch or more of precipitation in Akron is (a) exactly 17 days, (b) at most 17 days, and (c) more than 17 days.
8.The data show the daily high temperature in a town every day for a week. Mon Tue Wed Thu Fri Sat Sun 76∘F 78∘F 81∘F 74∘F 69∘F 69∘F 70∘F How can you find the experimental probability that the high temperature on a given day was warmer than 75∘F? Count the number of days with temperatures above 75∘F and divide that number by the number of days in the week. Count the number of days with temperatures below 75∘F and divide that number by .75∘F. Count the number of days with temperatures above 75∘F75∘F and divide that number by 75∘F. Count the number of days with temperatures above 75∘F and divide that number by the number of days with temperatures below 75∘F.
1.A husband and wife take out an insurance policy for a 20 year term. It is estimated the probability of being alive in 20 years time is 0.8 for the husband, and 0.9 for the wife. What is the probability that in 20 years time, just one of them will be alive. Explain your reasoning carefully.
6. Clinical trials have shown that 90% of the patients with severe migraine experience relief of their pain after taking the drug Nimodipine. Suppose 15 migraine patients try Nimodipine. a. What is the probability all of the patients experience relief? b. What is the probability only 10 patients experience relief? What is the probability at least 12 patients experience relief? d. What is the probability at most 10 patients experience relief? e. How many are expected to experience relief?
A typical fuel tanker can carry up to 40,000 L of fuel and can be loaded in about 20 minutes. The shift supervisor comes to check on one of the tankers, not knowing how much time is left in the fill process. a. What is the probability that there is less than 5,000 L remaining? b. What is the probability that there is between 15,000 L and 25,000 L of fuel remaining? c. What volume of fuel would the shift supervisor expect the tanker to contain? L
4.The mortality rate for a certain disease is 25%. A random sample of twelve patients with this disease is selected. a.What is the probability that exactly half of the patients selected will die from the disease? b.What is the probability that at least two of the twelve patients will die from the disease?
Suppose a math class contains 37 students. There are 19 females (six of whom speak Spanish) and 18 males (five of whom speak Spanish). Give all answers as decimals to at least two decimal places.1. What is the probability that a randomly selected student speaks Spanish, given that the student is female? 2. What is the probability that a randomly selected student does not speak Spanish, given that the student is male? 3. What percent of Spanish speaking students are male? 4. If someone does not speak Spanish what is the probability they are female?
5.Approximately 64% of the people murdered actually knew their murderer. Given 63 current unsolved murders, what is the probability that at least (equal to and more than) 35 victims knew their murderer?
12. A survey conducted discovered that 63% of all Americans are overweight. Suppose that a number of randomly selected Americans are weighed. The following table may (or may not) be useful: k 0 1 2 3 4 1 4 6 4 1 4Ck (a) Find the probability that the 4th person weighed is the first person to be overweight. (b) Find the probability that it takes less than 4 people to observe the first overweight person. (c) Find the expected value and variance of the number of Americans that would have to be weighed in order to find the first person that was overweight.

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