I. PROBLEM SOLVING. Show complete solutions. Label graphs completely. Save filename as lastname_act3.pdf 1. The orders from n = 100 customers for wooden panels of various thickness (X) are summarized as follows: Wooden Panel Thickness (X; inches) 1/4" 70 1/8" | No. of customer orders 3/8" 10 20 a) Determine the probability distribution. Graph f(x). b) Determine the cumulative distribution plot x vs f(x).

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Chapter1: Combinatorial Analysis
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PROBLEM SOLVING. Show complete solutions. Label graphs completely. Save filename as
lastname_act3.pdf
I.
1. The orders from n = 100 customers for wooden panels of various thickness (X) are summarized
as follows:
Wooden Panel Thickness (X; inches)
1/8"
20
1/4"
3/8"
No. of customer orders
70
10
a) Determine the probability distribution. Graph f(x).
b) Determine the cumulative distribution plot x vs f(x).
2. A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3
of the sets.
a) If x is the number of defective sets purchased by the hotel, find the probability distribution of
x. Express the results graphically as a probability histogram.
b) Find the cumulative distribution function of the random variable X representing the number
of defectives. Then using f(x), find (a) p(X = 1); (b) p(0< X < 2).
3. Suppose that the probability density function of x is
f(x) = {3x², 0 <x < 1)
0,
elsewhere)
a) Determine p(x < (1/3)), p((1/3)< x < (2/3)), and p(x > (2/3))
b) Determine the cumulative distribution function of x.
Transcribed Image Text:PROBLEM SOLVING. Show complete solutions. Label graphs completely. Save filename as lastname_act3.pdf I. 1. The orders from n = 100 customers for wooden panels of various thickness (X) are summarized as follows: Wooden Panel Thickness (X; inches) 1/8" 20 1/4" 3/8" No. of customer orders 70 10 a) Determine the probability distribution. Graph f(x). b) Determine the cumulative distribution plot x vs f(x). 2. A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. a) If x is the number of defective sets purchased by the hotel, find the probability distribution of x. Express the results graphically as a probability histogram. b) Find the cumulative distribution function of the random variable X representing the number of defectives. Then using f(x), find (a) p(X = 1); (b) p(0< X < 2). 3. Suppose that the probability density function of x is f(x) = {3x², 0 <x < 1) 0, elsewhere) a) Determine p(x < (1/3)), p((1/3)< x < (2/3)), and p(x > (2/3)) b) Determine the cumulative distribution function of x.
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