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- According to an article, 74% of high school seniors have a driver's license. Suppose we take a random sample of 100 high school seniors and find the proportion who have a driver's license. Find the probability that more than 76% of the sample have a driver's license. Begin by verifying that the conditions for the Central Limit Theorem for Sample Proportions have been met. The probability that more than 76% of the sample have a driver's license is...?Suppose surveys by ABC team and XYZ team indicate that 44% of voters support the secession of company. Suppose further that a intern takes a sample of 20 random voters. 1. Using Bernoulli random variable, construct the probability distribution for each possible outcome on the number of independent company supporters out of the 20 individuals using the binomial formula and solve for the first and second moment. Expand the table as necessary. 2. Draw the PDF/PMF graph and label the first momentThree distinct integers are chosen at random from the first 20 positiveintegers. Compute the probability that: (a) their sum is even; (b) their product iseven.
- According to recent reports, currently 39% of the population of NC (adults and children) has been fully vaccinated against Covid. Suppose of random sample of 400 individuals from the population of NC is selected. Let x represent the number in the sample who are fully vaccinated. a. State the values of n and p for this binomial experiment. b. Find the probability that exactly 156 in the sample have been fully vaccinated. Round to 4 decimal places.A binary communication channel transmits a sequence of "bits" (0s and 1s). Suppose that for any particular bit transmitted, there is a 20% chance of a transmission error (a 0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of one another. Consider transmitting 1000 bits. What is the approximate probability that at most 225 transmission errors occur? Suppose the same 1000-bit message is sent two different times independently of one another. What is the approximate probability that the number of errors in the first transmission is within 50 of the number of errors in the second?A machine randomly generates 1 of 9 numbers, 1...9, with equal likelihood. What is the probability that when John uses this machine to generate four numbers their product is divisible by 14? Express your answer as a common fract
- . A frog is performing a random jump on a Pentagon(5 sides) starting from corner 1. For each jump, it jumps with equal probability to one of the two adjacent corner with equal likelihood. The frog repeats this process until it returns to the corner where it began. When this ends, what is the probability that the frog has jumped on every corner of the pentagon? How would you generalize this case for a frog jumping on the corners of an n-sided polygonA maths examination consists of two papers, which are marked independently. Themark given for each paper can be any integer from 0 to 50 inclusive, and the total markfor the examination is the sum of the marks on the individual papers. In order to makethe examination completely fair, the examiners decide to allocate the marks for each paperat random, so that the probability of a given candidate being allocated k marks where0 < k < 50) for a given paper is 1/51.Show that the probability of a given candidate receiving a total of 60 marks in total onthe two papers is41/51^2To Construct:Random Variable X such that its first 2n moments exist and rest of the moments don't exist