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Unformatted text preview: STAT 1000 Assignment 3 DUE: February 29th (Wed. Eve. Section), March 1st (T/Th. Sections), March 2nd (MWF. Sections) SHOW ALL YOUR WORK 1. [4] A variable X has a distribution which is described by the density curve shown below: (a) What proportion of observations of X are less than 5? Solution: The area of the rectangle (base * height) between 2 and 5 is (5 2)(0 . 2) = 0 . 6 and the area of the rectangle less than 2 is (2 0)(0 . 1) = 0 . 2. Therefore, summing them the proportion of observations less than 5 is 0.8. (b) What proportion of observations are between 2 and 4? Solution: The area of the rectangle between 2 and 4 is: (2)(0 . 2) = 0 . 4 2. [2] A random variable X has a triangular distribution on the interval 5 to 10. What must the height be in order for this to be a true density curve? Solution: The area of a triangle is ( b )( h ) 2 . We know the area under all density curves is equal to 1. Therefore, 1 = (10 5)( h ) 2 , h = 2 5 3. [1] A telemarketing firm in a certain city uses a device that dials residential telephone numbers in that city at random. Of the first 100 numbers dialed, 51% are unlisted. This is not surprising because 48% of all residential phone numbers in this city are unlisted. Explain whether the percentages in bold are either a statistic or parameter. Solution: 51% is the statistic , this value is obtained from the sample. 48% is the parameter , this value is the statement about the population. 4. [11] Let Z follow a standard normal distribution, find the following proportions: (a) P ( Z < . 50) Solution: P ( Z < . 50) = 0...
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 Spring '12
 XU

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