Consider a Poisson distribution with a mean of two occurrences per time period. a. write the appropriate Poisson probability function. b. what is the expected number of occurrences in three time periods? c. write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods. d. Compute the probability of two occurrences in one time period. e. Compute the probability of six occurrences in three time periods. f. Compute the probability of five occurrences in two time periods.

A poll reported that 63% of adults were satisfied with the job the major airlines were doing. Suppose 25 adults are selected at random and the number who are satisfied is recorded. Complete parts (a) through (e) below. (c) Find and interpret the probability that at least 20 of them are satisfied with the airlines. The probability that at least 20 adults are satisfied with the airlines is (Round to four decimal places as needed.) Interpret the probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) OA. In 100 randomly sampled surveys of 25 adults, 20 or more of the 25 adults would be expected to be satisfied with the airlines in about B. In 100 randomly sampled surveys of 25 adults, less than 20 of the 25 adults would be expected to be satisfied with the airlines in about OC. In 100 randomly sampled surveys of 25 adults, exactly 20 out of the 25 adults would be expected to be satisfied with the airlines in…

Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15   Is this model a probability distribution? A. Yes. B. No. C. Maybe.

Power failures occur at an electric plant on average 3 times per year. If we can assume this follows a Poisson distribution, answer the following questions. a. What is the probability that there are 4 power failures in 2021? b. What is the probability that there are no more than 2 power failures in a given year? c. How likely is it that there are at least 3 power failures next year?

Suppose that births in a hospital occur randomly at an average rate of 1.9 births per hour. Assume that the probability of a birth is the same for any two time intervals of equal length. a.    Which distribution can we use in this case? b.    What is the probability that we observe at least 3 births in a 2-hour interval?c.    Suppose that births occur randomly in hospital A and hospital B at an average rate of 2.1 births and 3 births per hour, respectively. What is the probability that we observe 7 births in total from the two hospitals in a 1-hour period?

A. Recent crime reports indicate that 0.5 motor vehicle thefts occur each minute in an industrial area. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution. i. What is the average number of motor vehicle thefts occurring in five minutes? ii. Find the probability exactly three motor vehicle thefts occur in five minutes. Note: 1.Please clear answer no (i,ii) 2. No need excel formula.

Q3. A 10-year record of tornadoes per year to land in a particular region is 2, 2, 1, 3, 2, 1, 0, 2, 3, and 1. Using Poisson's distribution, what is the probability of not having tornados in any 1 year? What are the average of the number of tornadoes in 1 year?

It has been observed that the average number of accidents that occur on an assembly line is 3 per week. Find the probability that: i. A particular week will be accident free. ii. At least three (3) accidents will occur in a week. iii. Exactly five (5) accidents will occur in two week