Use the poisson distribution  approximate the case where the chance of success is p = 0.01 and the number of trials is n = 1000 in the following binomial probability problem: Part A. Pr(x = 10) Part B. Pr(x ≤ 10) Part C. Pr(x ≤

A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 3 cars needs to have oil added. If this is true, what is the probability of each of the following: (a) What is the probability that at least two of the next 5 cars need oil? Probability = (b) What is the approximate probability that between 181 and 216 of the next 600 cars need oil (Use the Normal approximation technique)? Probability =

Use the poisson distribution x! to approximate the case where the chance of success is p = 0.01 and the number of trials is n = 1000 in the following binomial probability problem: Part A. Pr(x = 10) %3D Part B. Pr(x < 10) Part C. Pr(x < 2)

Suppose that a pair of fair dice are rolled 120 times. Let X be the number of rolls on which the sum of the two numbers is 12. Show your working details. You may use R to verify your answer. (a) Find the probability when X = 3 approximately using Poisson approximation. (b) Compute the actual probability from binomial distribution. Comment on the accuracy of Poisson approximation.

I want a solution in steps

For the probability distribution of a discrete random variables, the sum of the probabilities of all possible values of x is always

Suppose a random variable x is best described by a uniform probability distribution with a range 0 to 5. Find the value of a that makes the following probability statements true.

What do i specifically put in the box as p(x)=

Why is the probability that a continuous random variable equals a specific number zero?  That is, why is P(X=b)=0 for any number b?