For n = 4 and I: = 0.80, what is P(X = 3)? P(X = 3) = D (Round to four decimal places as needed.) Determine the mean and standard deviation of the variable X in the binomial distribution where n = 4 and I: = 0.50. Determine the mean. ll = E (Type an integer or a decimal.) A student is taking a multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question There are ve multiple-choice questions on the exam. Complete parts (a) through (d) below. a. What is the probability that she will get ve questions correct? (Round to four decimal places as needed.) A manufacturing company regularly conducts quality control checks at specied periods on the products it manufactures Historically, the failure rate for LED light bulbs that the company manufactures is 11%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts (a) through (d) below. a. What is the probability that none of the LED light bulbs are defect'we? The probability that none of the LED light bulbs are defective is . (Type an integer or a decimal. Round to four decimal places as needed.) Suppose that you and two friends go to a restaurant, which last month filled approximately 79% of the orders correctly. Complete parts (a) through (d) below. . . . a. What is the probability that all three orders will be filled correctly? The probability is (Round to four decimal places as needed.)Assume a Poisson distribution with 2 = 4.4. Find the following probabilities. a. X = 1 b. X 1 d. Xs 1Assume that the number of new visitors to a website in one hour is distributed as a Poisson random variable. The mean number of new visitors to the website is 2.1 per hour. Complete parts (a) through (d) below. a. What is the probability that in any given hour zero new visitors will arrive at the website? The probability that zero new visitors will arrive is (Round to four decimal places as needed.) Over a period of three months during one year, an airline's rate of involuntarily denying boarding was 0.89 per 10,000 passengers. Complete parts (a) through (c) below. E> a. What is the probability that in the next 10,000 passengers, there will be no one involuntarily denied boarding? The probability that there will be no one involuntarily denied boarding is (Round to four decimal places as needed.) A company publishes statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For one year, Car A had 1.38 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model Aoar. Complete parts (a) through (d). a. What assumptions must be made in order for X to be distributed as a Poisson random variable? Select all the assumptions for a Poisson distribution. I: A. At least 30 model A cars are sold. I: B. The number of problems in a given period is independent of the number of problems in any other period. I: C. The probability of a problem in a time period approaches zero as the length of the time period becomes smaller. I: D. The probability of a problem is the same for each period of time