m16812 Continuous Random Variables: Practice 1 1.10 2008/06/13 13:06:01 GMT-5 2009/02/18 19:46:32.508 US/Central Susan Dean Susan Dean deansusan@deanza.edu Barbara Illowsky Dr. Barbara Illowsky illowskybarbara@deanza.edu Susan Dean Susan Dean deansusan@deanza.edu Barbara Illowsky Dr. Barbara Illowsky illowskybarbara@deanza.edu Connexions Connexions cnx@cnx.org Maxfield Foundation Maxfield Foundation cnx@cnx.org continuous distribution elementary exercise function graph homework practice probability random statistics uniform variable Mathematics and Statistics In this module the student will explore the properties of data with a uniform distribution. en Download handout (.doc) Download handout (.pdf)

The student will explore the properties of data with a uniform distribution.

The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

What is being measured here? The age of cars in the staff parking lot In words, define the Random Variable X size 12{X} {} . X size 12{X} {} = The age (in years) of cars in the staff parking lot Are the data discrete or continuous? Continuous The interval of values for X size 12{X} {} is: 0.5 - 9.5 The distribution for X size 12{X} {} is: X size 12{X} {} ~ U ( 0 . 5,9 . 5 ) size 12{U \( 0 "." 5,9 "." 5 \) } {}

Write the probability density function. f ( x ) size 12{f \( x \) } {} = 1 9 size 12{ { {1} over {9} } } {} Graph the probability distribution. aSketch the graph of the probability distribution.

bIdentify the following values: iLowest value for X size 12{X} {} : iiHighest value for X size 12{X} {} : iiiHeight of the rectangle: ivLabel for x-axis (words): vLabel for y-axis (words): b.i0.5 b.ii9.5 b.iiiAge of Cars b.iv 1 9 size 12{ { {1} over {9} } } {} b.v f ( x ) size 12{f \( x \) } {}

Find the probability that a randomly chosen car in the lot was less than 4 years old. aSketch the graph. Shade the area of interest.

bFind the probability. P ( X < 4 ) size 12{P \( X<"5730" \) } {} = b. 3 . 5 9 size 12{ { {3 "." 5} over {9} } } {} Out of just the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than 4 years old. aSketch the graph. Shade the area of interest.

bFind the probability. P ( X < 4 ∣ X < 7 . 5 ) size 12{P \( X<4 \lline X<7 "." 5 \) } {} = b 3 . 5 7 size 12{ { {3 "." 5} over {7} } } {} What has changed in the previous two problems that made the solutions different?

Find the average age of the cars in the lot. μ size 12{μ} {} = 5 Find the third quartile of ages of cars in the lot. This means you will have to find the value such that 3 4 size 12{ { {3} over {4} } } {} , or 75%, of the cars are at most (less than or equal to) that age. aSketch the graph. Shade the area of interest.

bFind the value k size 12{k} {} such that P ( X < k ) = 0 . 75 size 12{P \( X<k \) =0 "." "75"} {} . cThe third quartile is: b k size 12{k} {} = 7.25