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Unformatted text preview: UF-ESI-6321 UF-ESI-6321-02-32.xmcd page 1 of 2 2.32 It is estimated that f := 80 % of all customers at Speedy Pizza prefer thin crust pizza to thick crust pizza. The remaining g := 20 % prefer thick crust pizza to thin crust pizza. Of the many orders received by Speedy Pizza on a Friday night, six separate orders fail to mention the type of crust desired. Unable to contact the six customers and hoping to minimize disappointments, the manager of Speedy Pizza has decided to send all of the six customers thin crust pizzas. (a) Let X be the number of customers (among the six) who prefer the thin crust pizza. What assumptions must be satisfied in order for X to obey a binomial distribution? 1. A sequence of n independent trials established the distribution such that it applies to n = 6. 2. Each trial has exactly two outcomes of success or failure where "success" means "customer chooses thin crust" and "failure" means "customer chooses thick crust." 3. The probability of "success" is the same value p for each trial and the probability of "failure" is 1 - p for each trial -- in this case p = 0.8 and 1 - p = 0.2. (b) Write down the probability distribution of X. Let p equal the success of a randomly selected customer choosing thin crust. p := 80% n := 6 X := 0 .. n P( p , n , x) := n! x! ( n - x)! p (1 - p )
x n- x P( p , n , X ) = 0.01 0.15 1.54 8.19 24.58 39.32 26.21 % Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 UF-ESI-6321 UF-ESI-6321-02-32.xmcd page 2 of 2 (c) What is the probability that exactly three of the six customers will prefer thick crust pizza, and so be unsatisfied? p' := 20% x := 3 P( p' , n , x) = 8.19 % (d) What is the expected number of customers who will prefer thin crust pizza? n p = 4.80 What is the standard deviation of the number of customers who will prefer thin crust pizza? := n p (1 - p ) = 0.98 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 ...
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- Spring '07
- Normal Distribution, Kennedy Space Center, Speedy Pizza, crust pizza