Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a a = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter µ = 8t. a) What is the probability that exactly 6 small aircraft arrive during a 1- hour period? At least 6? At least 10? b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period?

The number of babies in a litter of rabbits is approximately Poisson distribution with mean 6. Litters can occur once per month for a 9 month period (3 months infertile). What is the standard deviation of the number of babies in one litter? What is the probability of a litter with exactly one rabbit? What is the approximate probability that over a 9 month period, a rabbit will have more than 65 babies (use the Central Limit Theorem, continuity correction is optional)? Incidentally, the plot at right shows the exact Poissondistribution you’ll be using, and you’ll note it looks quite a bit like some other distribution . .

Let x be a random variable that represents the weight of a lion in a certain region of Africa. Assume that x is normally distributed with a mean = 260 lbs . With standard deviation =30 lb  Please include the graphs for questions A and B

the weekly amount of money spent on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed with a mean u= $615 and standard deviation of $42.   A) if $646i budgeted for next week, what is the probability the actual costs will exceed the budgeted amount?   B) how much should be budgeted for weekly repairs, cleaning and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.10?

Use this information about the overhead reach distances of adult females: µ = 205.5 cm, σ = 8.6 cm, and overhead reach distances are normally distributed (based on data from th Federal Aviation Administration) If 40 adult females are randomly selected, find the probability that they have a mean overhead reach between 204.0 cm and 206.0 cm.

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in thedusLove uo useful life (150,000 miles of driving) of cars of a particular model varies Normall/ih nean 80 mg/mi and standard deviation 4 mg/mi. A company has 25 cars of this model in its et find the level L such that the probability that the average NOX+NMOG level 7 for the fleet is greater than L is only 0.01. Give your answer to three decimal places.