Department of Mathematics & Statistics STAT 2593 Midterm ...

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$MATH 0863 - PRECALCULUS - University of New Brunswick$

$2012 Science Atlantic Math Competition$

Suppose that 30% of all desktop computers in use today are made by the Dingle Brand ComputerCompany. Suppose that the probability that a desktop computer has at least one crash during anygiven month is 0.15. Let D be the event that a randomly chosen desktop computer is a Dingle Brandmachine, and let C be the event that that computer has at least one crash this month. What is thevalue of P (D ∩ C):17. If D and C are independent?0.04518. If D and C are mutually exclusive?019. If P (D ∪ C) = 0.35?0.120. If P (C|D) = 0.2?0.0621. If P (D|C) = 0.2?0.0322. If D ′ and C are mutually exclusive?0.1523. If D ′ and C are independent?0.045Of the eggs sold as “cracked” in New Brunswick, only 20% actually have discernible cracks.24. Suppose that you buy a “half-carton” of these so-called cracked eggs (i.e. 6 such eggs). Assumethat the six eggs in the carton constitute a random sample from the population of all eggswhich are sold as “cracked”. What is the probability that precisely two of the eggs in yourhalf-carton have discernible cracks?0.24586
25. Under the given assumptions the probability that a half-carton of eggs contains no eggs withdiscernible cracks is 0.2621 (to 4 decimal places). How many half-cartons would you expect tobuy before getting one entirely free of eggs with discernible cracks? (NOTE: “before” meansthat you don’t count that first “good” carton amongst the ones you buy.)2.815326. What is the probability that you buy at least seven half-cartons before you get one which isentirely free of eggs with discernible cracks?0.1191Cubical crystals of a certain substance have an edge length in mm with probability density functionequal tof(x) = 11.375 × 1 x 2 for 0.5 ≤ x ≤ 1.6(f(x) ≡ 0 elsewhere).27. What is the expected volume of such a crystal?0.84Let X denote the amount of time for which a book on 2 hour reserve is checked out of the Engineeringlibrary by a randomly selected student. Suppose that X has cumulative distribution function⎧⎨ 0 x ≤ 0F (x) =2x⎩ 3 − x290 ≤ x ≤ 31 x ≥ 328. What is the probability that the student has to pay a fine? (I.e. what is the probability thatthe student brings the book back after more than 2 hours?)1/9 = 0.111129. What is the probability density function of X? (Be sure to specify the value of this p.d.f. forall values of x.)2/3 − 2x/9 0 ≤ x ≤ 3, 0 elsewhereSuppose that the time that a randomly selected Engineering professor keeps a book (on “regularloan”) from the Engineering library is Gamma distributed with mean 49 days, and standard deviation14 days.30. What is the value of β (i.e. “shape parameter” or in Minitab terminology “second shapeparameter”) for this distribution?47
Page 1 and 2: Blue paper.Department of Mathematic
Page 3 and 4: 8. What is the probability that an
Page 5: A stem-and-leaf plot of these data

Department of Mathematics & Statistics STAT 2593 Midterm ...

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