(a) A fire-detection device utilizes three temperature-sensitive cells acting in-dependently of each other in such a manner that any one or more may ac-tivate the alarm. Each cell possesses a probability p = 0.8 of activating thealarm when the temperature reaches 100 degrees Celsius. Let Y equalthe number of cells activating the alarm when the temperature reaches100 degrees. Find the probability distribution of Y. Find the probabilitythat the alarm will function when the temperature reaches 100 degrees.(b) A geological study indicates that an exploratory oil well should strike oilwith probability 0.2. What is the probability that the third strike comes onthe seventh well drilled? What assumptions did you make to obtain thisanswer?

Answered: Image /qna-images/answer/483f3550-0c6e-4ef8-af69-294a23e7225f.jpg

Answered: (a) A fire-detection device utilizes…

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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Adult men's heights (in inches) are normally distributed with μ = 70 and σ = 3. Adult women heights (in inches) are normally distributed with μ = 67 and σ = 2. Members of the "Beanstalk Club" must be at least six feet (72 inches) tall. (a) If a man is selected at random, what is the probability that he is eligible for the Beanstalk Club? (b) If a woman is selected at random, what is the probability that she is eligible for the Beanstalk Club?
Suppose the Road Transport and Safety Agency (RTSA) officers have mounted a checkpoint and they observe the speed at which the cars pass through that check point.Assume the speeds are normally distributed such that µ = 61 km per hour and σ = 4km per hour.(a) Calculate the probability that the next car that passes through the checkpoint willbe travelling slower than 65 km per hour.(b) Calculate the probability that the next car passing will be travelling more than 66
Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 20 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 25 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 33 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.Wq = 2.797 minutes Hire a second person to…
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…
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
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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 = 9.9 mg/L with 95% of the data ranging from 6.3 mg/L to 13.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has 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…
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by

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