1). Define the random variable x to be the time you get home on Thursday.
a) Is x a discrete or continuous random variable? Explain.
b) Sketch a graph of the probability function f(x). Explain how you determined the shape of the graph.
2). The table below gives the size of the freshman class entering BSC for the past several years.
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Class of
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2005
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2006
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2007
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2008
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2009
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2010
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2011
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2012
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2013
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2014
|
|
Size
|
1178
|
1297
|
1304
|
1305
|
1332
|
1361
|
1584
|
1502
|
1479
|
1460
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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a) Compute the expected value of the size of the freshman class. (Assume each size listed above is equally likely).
b) Compute the standard deviation of the size of the freshman class.
c) Based on your answers to part (a) and (b), would you say that the size of the freshman class at BSC was extremely variable or fairly constant over the last ten years? Explain your reasoning.
3). The U.S. Air Force has designed a missile detection system which will detect 19 out of 20 incoming missiles. If one early warning system is good, two must be better; "how much better?".
a) What is the probability that 1 detection system will detect an incoming missile?
b) If 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the missile?
c) If 3 systems are installed, what is the probability that at least 1 of the systems detects the missile?
d) How many detection systems would you recommend operating? Why?
4). Suppose the average height of a female freshman at BSU is 65 inches and the standard deviation is 5 inches. Define a random variable x whose value is the height of a randomly selected freshwoman.
a) How would you model x? (Binomial, poisson, uniform, normal, exponential or other?)
b) Use that model to estimate the percentage of female freshmen under 60 inches tall.
c) Fill in the blank: 90% of female freshmen at BSU are over ______ inches tall.
5). Between 4 and 9 PM, cars place orders at the drive through window of the Tiki Takeout restaurant once every 5 minutes. The worker who processes those orders gets a ten minute break every two hours.
a) What is the probability of receiving 20 drive through orders in one hour?
b) What is the probability of there being a ten minute gap between orders?
c) Calculate the probability of receiving fewer than 2 orders in ten minutes.