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MPZ 3132-Engineering Mathematics IB Assignment No.04 - Academic Year – 2010 Instructions • Answer all questions • Please send the answer scripts of your assignment on or before the due date to the following address. Course Coordinator – MPZ 3132 Dept. of Mathematics & Philosophy of Engineering Faculty of Engineering Technology The Open University of Sri Lanka. Nawala, Nugegoda • Write your address back of your answer scripts • Use both sides of paper when you are doing assignment. You can collect model answers from virtual class(www.ou.ac.lk) User name - student0 Password - MPZ3132 (1). (a) Find the following probability for a standard normal random variable z. (ii) P(− 9 ≤ z ≤ 0 ) (i) P(0 ≤ z ≤ 1.2 ) (iii) P(0.3 ≤ z ≤ 1.56 ) (iv) P(− 1.56 ≤ z ≤ −2 ) (b) (i) Find the value of a such that P (− a ≤ z ≤ a ) = 0.90 (ii) Find the value of b such that P(− b ≤ z ≤ b ) = 0.99 (iii) Find the value of c such that P (z ≤ c ) = 0.8643 (c) The random variable X follows the binomial B (n, p ) distribution with probability mass n x n− x function f ( x ) = p q x = 0,1,...., n , o < p < 1 , where q = 1 − p . x Show that E ( x ) = np and var( x ) = npq A mathematical class in a school is divided in to set A with 12 students and set B with 25 students. Both groups are given a test consisting of 16 short questions. For any student in set A, the score (that is the number of correct answers) is distributed as B(16,0.75) for any student in set B, the score is distributed as B(16,0.5).All students answer independently. Find the probability that, (i) A given set A student gets all 16 questions right. (ii) At least one student in set A gets all 16 questions right (2) (a) The random variable X has a Poisson distribution with parameter λ so that

P ( X = x) =

e− λ

λx

x!

, x = 0,1, 2,...

.

(i) Find E ( x )

0 , o/w (ii) If P ( X = K ) = P ( X = K + 1) where K is some integer, show that λ must be the integer (K + 1)

1

(iii)In the manufacture of curtain material,...

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