A sample of a radioactive material is studied in a lab. There are an average of 2.6 gamma ray emissions per second. Use the Poisson distribution to find the probability that exactly 2 gamma rays are emitted in a single second. Do not round intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)
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- Use excel sheet to find The number of gamma rays emitted per second by a certain radioactive substance is a random variable having the Poisson distribution with (λ)= 5/8. If a recording instrument becomes inoperative when there are more than 12 rays per second, what is the probability that this instrument becomes inoperative during any given second?A major hotel chain keeps record of the number of customer complaints per week. In a recent year, the hotel chain had 5 complaints per week. Assume that the number of complaints follows a Poisson distribution. What is the probability the hotel will receive more than two complaints in the next week?The mean number of customers arriving at a service station during the 25-minute period is 5. Find the probability that 3 or more customers will arrive at the service station during a 25-minute period. Assume that the service system can be modeled as a Poisson distribution
- A technology company uses the Poisson distribution to model the number ofexpected network failures per month. It has been detected that, on average,there are 3 network failures per month1) What is the probability that the company experiences 2 of network failuresin a given month.2) What is the probability that the company experiences less than 4 networkfailures in a given month.3) What is the probability that the company experiences between 2 to 4network failures in a given month.4) On average, how many days elapse between two failures? (suppose that amonth has 30 days).5) Note that the waiting time that a network fails follows an exponentialdistribution with a decay parameter λ = 1. What is the probability thata network fails within 3 days?A rare genetic disease is known to be carried by DD people among 10000 people in the society.a) In a random sample of 1000 people, calculate the probability that less than GG carry the disease? (Pleasesolve this section with Binomial distribution)a) In a random sample of 2000 people, calculate the probability that more than HH carry the disease? (Pleasesolve this section with Poisson distribution)c) If people are randomly tested for the disease, what is the probability that the first person who is found tocarry the disease is the LL person?A source of liquid is known to certain bacteria with the mean number of bacteria per ce equal to 3. Ten 1 ce test tubes are filled wit the liquid. Using Poisson distribution, calculate the probability that all the test tubes will show growth, ie, at least 1 bacteria is contained in each
- A rare genetic disease is known to be carried by 20 people among 10000 people in the society.a) In a random sample of 1000 people, calculate the probability that less than 2 carry the disease? (Pleasesolve this section with Binomial distribution)a) In a random sample of 2000 people, calculate the probability that more than 5 carry the disease? (Pleasesolve this section with Poisson distribution)c) If people are randomly tested for the disease, what is the probability that the first person who is found tocarry the disease is the sixth person?In a specific area, this period of time, it is believed that the number of thunderbolts that are falling is distributed according to the Poisson distribution with a rate of 75 thunderbolts per hour. In the next questions give your answer as a decimal number correct in three decimal places. During a specific minute time, find the probability that: (i) there are no thunderbolts in the area.(ii) at least one thunderbolt hits the area.An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean 117 cm and standard deviation 5.2 cm. a) Find the probability that one selected subcomponent is longer than 120 cm. b) Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120 cm. c) Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.
- One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analysts generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switchboard arrive at an average rate of 2.4 calls per minute.a. If an operator wants to take a one-minute break, what is the probability that there will be no calls during a one-minute interval?b. If an operator can handle at most five calls per minute, what is the probability that the operator will be unable to handle the calls in any one-minute period?c. What is the probability that exactly three calls will arrive in a two-minute interval?d. What is the probability that one or fewer calls will arrive in a 15-second interval? a. P(x = 0 | λ = 2.4) = b. P(x > 5 | λ = 2.4) = c. P(x = 3 | λ = 4.8) = d. P(x ≤ 1 | λ = 0.6) =A shop sells an average of 3 pieces of mobile telephones every day, what’s the probability that they’ll sell 4 phones today? (Poisson distribution)In a recent year, a hospital had 4406 births. Find the mean number of births per day, then use that result and the Poisson distribution to find the probability that in a day, there are 15 births. Does it appear likely that on any given day, there will be exactly 15 births? The mean number of births per day is ___ (*Please before midnight!)