Ignore the wrong work. 11. In a study of brand recognition of the Kindle eReader
ID: 3325261 • Letter: I
Question
Ignore the wrong work. 11. In a study of brand recognition of the Kindle eReader, four consumers are interviewed. If x is the number of consumers in the in the group who recognize the Kindle brand name, then x can be either 0,1, 2,3, or 4. Assume the corresponding probabilities the consumers recognize the Kindle brand name are 0.026,0.252, 0.346, 0.246, and 0.130. Round answers to two decimal places, if necessary. Does the given information describe a probability distribution? Why or why not? a. yes, because T shows 4e (Gpaints) rar ot e Consumers who cogaze the Kindle brand Assuming the given information describes a probability distribution, find the mean. Round to two decimal places, if necessary. b. (3 points) 0,o 0.026 +0.252 10.3% +0.2461013 Assuming the given information describes a probability distribution, find the standard deviation. Round to two decimal places, if necessary. c.Explanation / Answer
x px x*px x*x*px 0 0.026 0 0 1 0.252 0.252 0.252 2 0.346 0.692 1.384 3 0.246 0.738 2.214 4 0.13 0.52 2.08 total 1 2.202 5.93 a) It is probability distribution because sum of all probabilities is 1. b) mean for this dprobability distribution = E(x) = sum(x*px) = 2.202 = 2.21 c) first find variance Var(x) = E(x^2) - [E(x)]^2 = sum(x*x*px) - [2.21]^2 = 5.93 - 4.8841 = 1.0459 now to find standard deviation : standard deviation is positive squarerrot of variance . Therefore standard deviation = squrt(1.0459) = 1.022 = 1.03