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Quiz_1_Solutions

Quiz_1_Solutions - Quiz#1 NAME K E MA 223 Engineering...

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Unformatted text preview: Quiz #1 NAME: K E \/ MA 223, Engineering Statistics Spring 2007-08; 10 points possible CM Box #2 Sections 1.1 — 1.3: Distributions Date: Monday, March 10 at the BEGINNING of class. l. [+0.5 each] Determine whether each of the following random variables is discrete or continuous. Circle the correct response. (a) The number of red cars in the RHIT parking lots on Friday. @} Continuous (b) The length of a piece of licorice randomly chosen from a Twizzler,bag\ ""“x. Discrete Continuous V5 (c) The number of pieces of hair you must pull from your head until you get a grey one. Discrete , Continuous (d) The lifetime of a randomly selected marker from our classroom. Discrete Comma ava City cash drawer at closing time on a given day. Discrete) Continuous (t) The time it took you to fall asleep last night once you laid down. Discrete @. 2. [+1 each] Suppose we gave the above 6 statements to a random sample of Wal-Mart shoppers this afternoon and asked them to identify the discrete and continuous variables. Let x denote the number of statements correctly indentiﬁed by a shopper. Suppose the probability mass function of x is given by: (e) The number of pennies in x: 0 1 2 3 4 5 6 p(x): 0.1 0.15 0.2 0.25 0.2 ? ?? (a) Determine the long-run proportion of shoppers that will get at most three statements correct. (b) Determine the long—run proportion of shoppers that will get at least 5 statements correct. ?/><2sl : l~ P/XeL/B : lie 2 9/0 3. [+1 each] I played volleyball last night; sometimes I have a hard time getting the ball over the net. Let x denote the number of the attempt on which I ﬁrst get the ball over the net. Suppose the probability mass function ofx is: 1006) = 0.1 . 09’“1 forx= 1, 2, 3, 4, (a) In the long run, what proportion of the games do I get the ball over on my ﬁrst attempt? an): 447)“: no (b) In the long run, what proportion of the games does it take me less than or equal to 3 attempts to get the ball over the net? ﬁxes): w + w» -+ W33 ’ o/ *t ,0? ~I .03! : 021/ 4. [+1, +2] Let x denote the response time (in seconds) at a certain on—line computer; that is, x is the time between the end of a user’s inquiry and the beginning of the system’s response to that inquiry. The value of x varies from inquiry to inquiry. Suppose the density ﬁinction of x is given by: _ 0.56‘0'5" x 2 0 ﬁx) _ { 0 otherwise. (a) What proportion of the inquiries have a response time of less than 4 seconds? ‘2’ _ ?(XU’): f.\’e“’”¢/.< —— O (b) State and support two reasons why this function is a valid density function for this continuous variable. ‘3 f ,S’e'ﬁck Z / Mame) 2} in) z o 4.1” W a (t, ma.) ...
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Quiz_1_Solutions - Quiz#1 NAME K E MA 223 Engineering...

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