Let X1, . . . , X5 be independent standard normal Random Variables. Compute the probability P(X1+…+X5 ≤ 5, X1^2+…X5^2 ≤ 10.824).
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Let X1, . . . , X5 be independent standard normal Random Variables. Compute the probability P(X1+…+X5 ≤ 5, X1^2+…X5^2 ≤ 10.824).
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- When circuit boards used in the manufacture compact disc players are tested, the long-run percentage of defectives is 5%. Let X the number of defective boards in a of random sample of size n= 25, so Bin(25, .05). a. Determine P(X 5). c. Determine P(1 < X < 4). d. What is the probability that none of the 25 boards is defective?Austin decided to give Taylor Swift another chance. So, he listened through all her songs from 2009. There were 8 in total. Let the random variable X be the number of songs in which she complained about some boy. The probability of complaining about a boy is 56%. *ONLY NEED HELP WITH D* a.) Is X a discrete or continuous random variable? How do you know? b.) What are the possible values of X? c.) What is the probability distribution function of X? D.) True or False? The probability that Taylor Swift complains about a boy in at least 2 songs equals the probability that Taylor Swift complains about a boy in more than 1 song?Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arival rate is 9 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no arrivals in a 15-second period (to 4 decimals). d. Compute the probability of at least one arrival in a 15-second period (to 4 decimals).
- The percentage of vehicles on a freeway that violate the speed limit is π = 0.88 You randomly clock n = 80 vehicles. 32) The probability that between 66 and 70 vehicles violate the speed limit is P(66 ≤ x ≤ 70) = a 0.4350 b 0.4438 c 0.4529 d 0.4621Suppose that X follows a Binomial distribution, i.e., X ∼ Binomial(3, 0.5). Define a new random variable as Y = X 2 , then, what is the value of the PMF of Y evaluated at 1, i.e., what is Pr(Y=1)? a). 0.3125 b). 0.25 c). 0.375 d). 0.5Let X denote the waiting time (in minutes) for a customer. An assistant manager claims that μ, the average waiting time of the entire population of customers, is 2 minutes with standard deviation also 2 minutes. The manager doesn't believe his assistant's claim, so he observes a random sample of 36 custoers. The average waiting time for the 36 customers is 3.2 minutes. What is the probability that the average of 36 customers is 3.2 minutes or more? Do you think that assistant manager's claim that the mean is 2 minutes is correct?
- 36) The time X needed to complete a final examination in a particular College Course is normally distributed with a mean of 60 minutes and standard deviatation of 10 minutes. The Probability of completing The exam in less than 70 minutes. is A) 0.9655. B)0, 1387 C) 0.8413 D) 0.0345An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (*) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X=2N -2. The values of X are given in the table below. Outcome ttt hth tht htt thh hhh hht tth Value of X -2 2 0 0 2 4 2 0 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the valuesof X. Then fill in the appropriate probabilities in the second row. Value x of X ___ ___ ___ ___ P(x=x) ___ ___ ___ ___Suppose the random variable X follows a normal distribution with mean 80 and variance 100. Then the probability is 0.6826 that X is in the symmetric interval about the mean between two numbers are A) -2 to 2 B) -3 to 3 C) -1 to 1 D) none
- Assume the flying height of an airplane is a Gaussian Random variable X with ax = 5000 m and ox=2000 m. Find the probability of the airplane flying higher than 10000 m. Use the table method.Suppose X is a random variable best described by a uniform probability distribution with C = 2 and d = 4. Find P(2.5 < X < 2.78). a) 0.14 b) 0.78 c) 0.39 d) 0.28The finish of a hole depends on the edge of the bit used, only 1% of the holes with a new drill have an irregular cut, 3% have an irregular cut with average bits and 5% present irregular cut with worn bits. If 25% of the holes are made with new bits, 60% have average edges and 15% are worn out. [use 3 decimal places] a) If a piece is taken at random, what is the probability of having holes irregular? b) If a piece with irregular holes is taken, what is the probability that would have been made with an average drill bit?
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