Find P(3≤x≤9), the probability that the dart lands in [3, 9].
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![A dart is thrown at a number line in such a way that it always lands in
[0, 10]. Let x represent the number the dart hits. Suppose the probability
1
density function for x is given by ƒ(x)=- x, for 0≤x≤10.
50
Find P(3 ≤ x ≤9), the probability that the dart lands in [3, 9].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F939f19e0-6626-477a-ba7a-4282434e880a%2Fe172ecef-98a0-40a5-96e5-8c7442de31c1%2Fdffk23_processed.png&w=3840&q=75)
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.The conditional probability of E given that F occur is P(EF)= _____________. So in rolling a die the conditional probability of the event E. “getting a six,” given that the event F, “getting an even number.” has occurred is P(EF)= ____________.Let X have a uniform on the interval (4, 9). Find the probability that the sum of 2 independent observations of X is greater than 16.
- Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.Let X have a uniform distribution on the interval (2, 10). Find the probability that the sum of 2 independent observations of X is greater than 19.Let x and y be randomly chosen from inside the circle with r = 4. For selected numbers, x+y≥ 4 and x2+y2≤16 Find the probability that the conditions will be met?
- The amount of time it takes Lexie to wait for the bus is continuous and uniformly distributed between 3 minutes and 16 minutes. What is the probability that it takes Lexie between 6 and 7 minutes given that it takes less than 11 minutes for her to wait for the bus? Provide the final answer as a fraction.Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then ? = 7500 and ? ≈ 1750.† A random sample of n = 50 workers from the toxic cleanup site were given a blood test that showed x = 6760. What is the probability that, for healthy adults, x will be this low or lower? (a) How does the central limit theorem apply? Explain. The central limit theorem describes the distribution of x as normal with mean ? x = 7500 and ? x ≈ 247.49.The central limit theorem describes the distribution of x as normal with mean ? x = 7500 and ? x ≈ 1750.00. The central limit theorem describes the distribution of x as normal with mean ? x = 7500 and ? x ≈ 35.00.The central limit theorem does not apply because the sample size is too small. (b) Compute P(x ≤ 6760). (Round your answer to four decimal places.) P(x ≤…A certain basketball team makes 70% of its free throws on average. In a game where the team shoots 40 free throws. what is the approximate probabillity that the number of free throws made by the team wilbe at least 25%
- Suppose that a number is randomly chosen from the interval (-3, 3). What is the probability that the value of x^2+2x−8 is negative? ROUND OFF your answer in DECIMAL FORM (4 decimal places)Five fourth‐grade children were selected at random from the entire class andtimed in a short race. The times in seconds were :6.3 4.2 4.7 6 5.7Test the hypothesis that the distribution of times is uniform on the intervalfrom 4 to 8 seconds. Note that such a distribuƟon is given by : F*(x) = 0 x < 4 =(x - 4)/4 4 equal to or less x < 8 =1 for for X 8 equal to or less x Use α = 0.10The probability that x lies between a and b is given by P( a≤ x≤ b) =Sba f(x) DX. Given f(x) = x3/5000 (10-x) for 0≤ x ≤ 10 and f(x) = 0 for all other values of x. Evaluate S100 f(x) dx
