6.(3pts)Estelle is grabbing a flashcard out of her box of eight (8).Some of the cards are white, and some are grey.Additionally, a triangle or circle are printed on some of each color, as shown in Figure 2. What is true about the eventsA: picking a grey card and B: picking a triangle if I were to choose one card at random?Figure 2: Color and Shape on Card in box.(a) The events are independent and mutually exclusive.(b) The events are independent and not mutually exclusive.(c) The events are not independent, but are mutually exclusive.(d) The events are neither independent nor mutually exclusive.

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Chapter 7 / Exercise 50

**Mathematical Applications for the Management, Life, and Social Sciences**

Harshbarger

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7.(3pts)Suppose you are interested in estimating the mean of a population of valuesμfrom a random sample of size 3.The variance of the population isσ2.Select the statement that best describes which estimator would you prefer. AssumeX1, X2andX3are iid random variables from the population. Would you prefer to use ˆμ1or ˆμ2?ˆμ1= 2X1-X2ˆμ2=X1+X2-X3?

8.(4 pts)Identify whether the random variable X in each of the following scenerios is a binomial random variable or not. Ifnot, in a few words explain what assumption[s] is[/are] not well met.(I) According to a recent study, 63% of children wear their bike helmets always, 24% wear them often, and 13% hardlyever wear them. If you interview 15 children, let X be the number that report hardly ever wearing a helmet.(II) You have a bag of 10 batteries, in which 2 are defective. Suppose you put 4 batteries into your calculator from thebag. Let X be the number of defective batteries in your calculator.