Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
The probability that a visitor to a Website provides contact data for additional information is 0.01. Assume that 1000 visitors to the site behave independently. Determine the following probabilities: (a) No visitor provides contact data. (b) Exactly 10 visitors provide contact data. (c) More than 3

Applied Statistics and Probability for Engineers 6
Consider the circuit in Example 2-34. Assume that devices fail independently. What is the probability mass function of the number of device failures? Explain why a binomial distribution does not apply to the number of device failures in Example 2-32. Eq

Applied Statistics and Probability for Engineers 6
Consider the time to recharge the lash in cell-phone cameras as in Example 3-2. Assume that the probability that a camera passes the test is \(0.8\) and the cameras perform independently. What is the smallest sample size needed so that the probability of at least one camera failing is at least \(95 \

Applied Statistics and Probability for Engineers 6
Problem 91E For each scenario (a)(j), state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make. (a) A production process produces thousands of temperature transducers. Let X denote the number of nonconforming transducers in a

Applied Statistics and Probability for Engineers 6
Let X be a binomial random variable with p = 0 2 and n = 20. Use the binomial table in Appendix A to determine the following probabilities. (a) \(P(X \leq 3)\) (b) \(P(X>10)\) (c) \(P(X=6)\) (d) \(P(6 \leq X \leq 11)\) Equation transcription: Text transcrip

Applied Statistics and Probability for Engineers 6
Let X be a binomial random variable with p = 0.1 and n = 10. Calculate the following probabilities from the binomial probability mass function and from the binomial table in Appendix A and compare results. (a) \(P(X \leq 2)\) (b) \(P(X>8)\) (c) \(P(X=4)\) (d) \(P(5 \leq X \leq 7)\)

Applied Statistics and Probability for Engineers 6
The random variable X has a binomial distribution with n = 10 and p = 0.5. Determine the following probabilities: (a) \(P(X=5)\) (b) \(P(X \leq 2)\) (c) \(P(X \geq 9)\) (d) \(P(3 \leq X<5)\) Equation transcription: Text transcription: P(X=5) P(X \leq 2) P

Applied Statistics and Probability for Engineers 6
The random variable X has a binomial distribution with n = 10 and p = 0.01. Determine the following probabilities. (a) \(P(X=5)\) (b) \(P(X \leq 2)\) (c) \(P(X \geq 9)\) (d) \(P(3 \leq X<5)\) Equation transcription: Text transcription: P(X=5) P(X \leq 2)

Applied Statistics and Probability for Engineers 6
Problem 96E The random variable X has a binomial distribution with n = 10 and p = 0.5. Sketch the probability mass function of X. (a) What value of X is most likely? (b) What value(s) of X is(are) least likely?

Applied Statistics and Probability for Engineers 6
Problem 97E Sketch the probability mass function of a binomial distribution with n = 10 and p = 0.01 and comment on the shape of the distribution. (a) What value of X is most likely? (b) What value of X is least likely?

Applied Statistics and Probability for Engineers 6
Determine the cumulative distribution function of a binomial random variable with n = 3 and p = 1/2.

Applied Statistics and Probability for Engineers 6
Problem 99E Determine the cumulative distribution function of a binomial random variable with n = 3 and p =1/4.

Applied Statistics and Probability for Engineers 6
Problem 100E An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates

Applied Statistics and Probability for Engineers 6
The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. (a) What is the probability that for exactly three calls, the lines are occupied?

Applied Statistics and Probability for Engineers 6
Problem 102E A multiple-choice test contains 25 questions, each with four answers. Assume that a student just guesses on each question. (a) What is the probability that the student answers more than 20 questions correctly? (b) What is the probability that the student answers fewer than 5 questions co

Applied Statistics and Probability for Engineers 6
A particularly long traffic light on your morning commute is green \(20 \%\) of the time that you approach it. Assume that each morning represents an independent trial. (a) Over 5 mornings, what is the probability that the light is green on exactly one day? (b) Over 20 mornings, what is the proba

Applied Statistics and Probability for Engineers 6
Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose that 15 samples are studied and can be considered to be independent for mutation. Determine the following probabilities. The binomial table in Appendix A can help. (a) No samples are mutated. (b) At most one sample

Applied Statistics and Probability for Engineers 6
An article in Information Security Technical Report [Malicious SoftwarePast, Present and Future (2004, Vol. 9, pp. 618)] provided the following data on the top 10 malicious software instances for 2002. The clear leader in the number of registered incidences for the year 2002 was the Internet worm Kle

Applied Statistics and Probability for Engineers 6
Problem 106E Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Suppose that 20 patients will visit an emergency room with

Applied Statistics and Probability for Engineers 6
Problem 107E A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (az) or 10 integers (09). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) one billion passwords from the potential set,

Applied Statistics and Probability for Engineers 6
Problem 108E Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more than 3 standard deviations. (a) If

Applied Statistics and Probability for Engineers 6
Problem 109E Because all airline passengers do not show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. (a) What is the probability that every pass

Applied Statistics and Probability for Engineers 6
Problem 110E This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 100 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically, 2% of the components are identified as defective, and the com

Applied Statistics and Probability for Engineers 6
Problem 111E Consider the lengths of stay at a hospitals emergency department in Exercise 3-33. Assume that five persons independently arrive for service. (a) What is the probability that the length of stay of exactly one person is less than or equal to 4 hours? (b) What is the probability that exact

Applied Statistics and Probability for Engineers 6
Consider the patient data in Example 2-8. Suppose that five patients are randomly selected with replacement from the total for hospital 4. Determine the following probabilities: (a) Exactly one is \(\text { LWBS }\). (b) Two or more are \(\text { LWBS }\). (c) At least one is \

Applied Statistics and Probability for Engineers 6
Problem 113E Assume that a Web site changes its content according to the distribution in Exercise 3-34. Assume that 10 changes are made independently. (a) What is the probability that the change is made in less than 4 days in 7 of the 10 updates? (b) What is the probability that the change is made in

Applied Statistics and Probability for Engineers 6
Problem 114E Consider the endothermic reactions in Exercise 3-32. A total of 20 independent reactions are to be conducted. (a) What is the probability that exactly 12 reactions result in a final temperature less than 272 K? (b) What is the probability that at least 19 reactions result in a final temp

Applied Statistics and Probability for Engineers 6
Consider the patient data in Example 2-8. Suppose that patients are randomly selected with replacement from the total for hospital 4. What is the smallest sample size needed so that the probability is at least 90% that at least one patient is LWBS? Example 2-8