Following graduation, you are hired as an assistant general manager for one of t
ID: 3231802 • Letter: F
Question
Following graduation, you are hired as an assistant general manager for one of the big casino firms in Reno. The casino wants to purchase 20 new gaming machines and wants you to provide statistical support for their purchasing decisions. International Gaming Technologies sells slot machines that are designed to pay-out once every 7 spins (1/7 or .143). However, an industry insider tells you that IGT made a mistake in their production line and some of the machines actually pay out once every 4 spins (1/4 or 0.25). Such flawed machines would be very bad for your boss's bottom line. 1. The probability of getting one of these flawed machines is 1/5 or 0.2. If your casino is purchasing 20 machines, the number of flawed machines you could expect to get would be drawn from what distribution? Answer:___ According to your boss' analyses, they can make $ off the new machines so long as no more than 2 of them are flawed. How many ways are there to get 2 flawed machines out of 20 purchases? Answer:____ What is the exact probability of getting no more than 2 flawed machines? What is the exact probability of getting more than 2 flawed machines?Explanation / Answer
a) no. flewed machines you could expect =n*p =20*0.2 =4
b)ways are get 2 flewed out of 20 machines =20C2 =20*19/2 =190
c)P(2) =P(0)+P(1)+P(2) =20C0 * 0.2^0*0.8^20 +20C1 * 0.2^1*0.8^19 + 20C2 * 0.2^2*0.8^18
= 0.8^20+20* 0.2^1*0.8^19 + 190*0.2^2*0.8^18
= 0.2060
d)exact probability of P(2) =1-0.2060 =0.794