The number of sales in a day for a small company is a gamma random variable that has a distribution with parameters a= 2 and b = 4. Find the probability for more than 5 sales on any given day. P(X > 5)

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 70.0 kg and standard deviation ? = 7.6 kg. Suppose a doe that weighs less than 61 kg is considered undernourished. (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 45 does should be more than 67 kg. If the average weight is less than 67 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 45 does is less than 67 kg (assuming a healthy population)? (Round your answer to four decimal places.)(d) Compute the probability that x< 71.8 kg for 45 does (assume a healthy population). (Round your answer to four decimal places.)

An elementary school keeps a record of the number of children sent to the office for disciplinary action. Table below X: 0, 1, 2, 3, 4, 5, P(X): 0.1, 0.2, 0.3, 0.2, 0.1, 0.1 Over a long period of time, the number xof children sent to the office per day had the probability distribution: (a)Find the probability that more than one(>1)childissent to the office per day. (b)Find the expected value ?of the number of children sent to the office in a day. (c)Find the standard deviation ?of the number of children sent to the office per day. Please help me with this homework problem! Thank you!

A drug tester claims that a drug cures a rare skin disease 77​% of the time. The claim is checked by testing the drug on 100 patients. If at least 69 patients are​ cured, the claim will be accepted.   Find the probability that the claim will be rejected assuming that the manufacturer's claim is true. Use the normal distribution to approximate the binomial distribution if possible.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 62.0 kg and standard deviation ? = 9.0 kg. Suppose a doe that weighs less than 53 kg is considered undernourished. (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 59 kg. If the average weight is less than 59 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 59 kg (assuming a healthy population)? (Round your answer to four decimal places.) Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was x = 63.8 kg. Do you think the doe population is undernourished or not? Explain. A. Since the sample average is above the mean, it…

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?

(1 point) Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace card, and draw another card. You repeat this process until you have drawn 20 cards in all. What is the probability of drawing at least 5 clubs? For the experiment above, let X denote the number of clubs that are drawn For this random variable, find its expected value and standard deviation. E(X) – Give your answers to at least 4 decimal places.

Data documented for weather events in the state of Montana is obtained over a period of years and includes hail storms causing property damage. The data is analyzed and appears to fit a poison distribution with an average of 3.3 damaging hail storms per year.  What is the likelihood that between 2 and 4 damaging hail storms are seen in a randomly selected year?  please show using Poisson.dist function  What is the probability that at least one significant hail storm causing damage is experienced in the coming year?  What is the likelihood that Montana would experience between 5 and 7 damaging hailstorms over a two year period?  What is the likelihood that Montana would experience more than 7 damaging hail storms over a two-year period? please show all steps using excel formulas

The number of x people entering the intensive care unit (ICU) at a particular hospital on any givenday has a Poisson probability distribution with mean equal to five persons per day. What is the probabilitythat the number of people entering the ICU on particular fay is less than equal to two?

The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter  ?y  for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?