Practice Final Exam

# Practice Final Exam - bulb tested the third bulb tested the...

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Statistics 416: Practice Final Exam 1. The percentage of impurities per batch in a certain type of industrial chemical has the PDF f ( x ) = kx (1 - x ) , 0 x 1 . A batch having more than 40% impurity cannot be sold. What percentage of batches cannot be sold for this reason? 2. The yield force of a certain type of steel reinforcing bar is normally distributed with a mean of 8,500 lbs. and a standard deviation of 80 lbs. If three bars are used in a certain job, what is the probability that all of them will yield forces in excess of 8,700 lbs.? 3. The grades in a standardized test are distributed normally with mean 70 and variance 81. Top 5% of the students are eligible to apply for a certain program. What is the minimum score required to be eligible to apply for this program? 4. A uniform random variable has mean 2.75 and variance 0.52. What is the probability that it is less than 3? 5. There are two good bulbs and two bad bulbs in a package. These will be tested one by one in a random order. Find the probability that the second bad bulb is the second
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Unformatted text preview: bulb tested; the third bulb tested; the fourth bulb tested. 6. A fair coin is tossed six times. Given that there are at least three heads, what is the probability that there are exactly four heads? 7. Billy, Silly, and Nilly shoot at a bull’s eye. They can hit the bull’s eye 70, 80, and 75% of the times, respectively. One of the three is known to have hit the eye. Find the probability that it was Nilly. 8. The scores of students in a standardized exam are normally distributed with mean 500 and standard deviation 100. (a) Jolly scored 654; what is her percentile score? (b) Billy scored 540; what is his percentile score? (c) Molly is at the 95th percentile of the score distribution; what is Molly’s score? 9. A normally distributed random variable has mean 40 and the probability that it is between 20 and 60 is 0.5. What is its variance? 1...
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