Section 7.6 10. Suppose that a probability distribution ha mean 10 and standard deviation Use the Chebychev inequality to estimate the probability that an outcome will lie between 9 and 11.
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- 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. _____minQ3 a) A component has an exponential time to failure with a mean of 100 hours. (i) The component has already been in operation for its mean life. What is the probability that it will fall by 150 hours? (ii) The component will operate for another 50 hours given that it is in operation 150 hours. (iii) If 20 components are tested, what is the probability that at least one fails in less than 200 hours? Assume that the components fail independently. b) Students of National University were classified according to their favorite color: Blue 12 5 Favorite color Red 13 13 Black 25 20 Male Female If one student is selected at random, then find the probability that the selected student: (i) Doesn't like black color. (ii) Is Female and likes blue color. (iii) Is Male or like black color. (iv) Likes red color given that it is female.Quantitave Methods 1 - Question 5
- Illustraiion 17.34. Mean of a distribution is 2.0. What are the probabilities corresponding to various successes 0, 1, 2,.., assuming that the Poisson distribution explains the data. If the total frequency1)When can a Standard Deviation for set of 5 numbers be zero? In other words, what kind of relationship must exist among all numbers in order for Standard Deviation to be zero Hint: Standard Deviation E(X¡ - Mean)²/(n – 1)17
- 18) Assume that adults have IQ scores that are normally distributed with a mean of 99.8 and a standard deviation of 20.1. Find the probability that a randomly selected adult has an IQ greater than 127.3. (Hint: Draw a graph.)Chapter 7: 6. The mean room and board expense per year at a four-year college is $9200. Assume the room and board expenses are normally distributed with a standard deviation of $1200. (6 points each) You randomly select one four-year college. What is the probability that their average room and board is less than $8950? b. You randomly select 50 four-year colleges. What is the probability that the mean average room and board is less than $8950?11. The probability that a mouse inoculated with a serum will contract a certain disease is 0.02. Using The Poisson approximation, find the probability taht at most 3 of 30 inoculated mice will contract the disease.
