28. Binomial distribution, n= 10, p= 0.5. a) Compute P(X = 5) b) Compute P(X> 5) c) Compute P(2
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- 5. Suggest any value, zo, of the standard normal probability distribution (correct to two decimal places), satisfying -1 -zo) and b) P (Z< 2z0)2. Let X ~ N (2856,16) a) What is the standard deviation of x? b) Calcuate P (X>7)6. Let X₁ be a r.v. having a Poisson distribution with mean 4, X₂be a random variable having a Poisson distribution with mean 2. What is the distribution of X₁+X₂ if both of the variables are independent? Show this by using MGF's. Find P(X₁+X227).
- Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution 4000. Determine the following in parts (a) and (b): with B 2 and 8 = = a P(X > 5000) b P(X> 8000|X > 3000) c Comment on the probabilities in the previous parts compared to the results for an expo- nential distribution.Suppose that the flight time from Chicago O'Hare International Airport to Hartsfield- Jackson Atlanta International Airport follows a uniform distribution with lower and upper bounds of 120 and 140 minutes, respectively. a) Suppose that Luke flies with Spirit Airlines, which posts a flight time of 2 hours and 5 minutes (that is, 125 minutes) for this route. What is the chance that his flight will be at most 5 minutes late? Hint: what is P(X < 130)? b) Let the flight duration be a random variable. Find the expected value and standard deviation of this variable.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) 0.0345
- Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x̅ = the average of the 49 races. A) Give the distribution x̅ (round your standard deviation to two decimal places.) x̅~______(______,______) B) Find the probability that the average of the sample will be between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.) C) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) ______ min D) Find the median of the average running times. _____min23. A variable is described at N(5,9). This indicates normal distribution, with Mean= 5 and Variance = 9. b) a) What are the corresponding Z values for X values of 2 & 5? What is the probability that X is less than 2? What is the probability that X is less than 5? c) C: What is the probability that X is between 2 and 5? e) What is the probability that Z < -1.24? d)Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
- a) A random variable has a binomial distribution. Findi) Its expexctationFind conditional probability Find mean and standard deviation 11)The age of customers at a local hardware store follows a uniform distribution over the interval from18 to 60 years old. Find the average age of customers to this hardware store. 140). 12) Suppose x is a uniform random variable with a = 20 and b = 80. Find the standard deviation of x. Find mean and standard deviationSuppose 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.
