Solutions to Ma381, Exam 2 (blue version), F04

Solutions to Ma381, Exam 2 (blue version), F04 - (16 pts...

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(16 pts.) Multiple Choice. For each problem, circle the singlebestresponse. 1. If X and Yare random variables and a,b,c are constants, then E(aX + bY + c) = a E(X) + b E(Y) + c (~:;!~~r~' , b. Sometimes c. Never 2. If X and Yare independent random variables anda,b,c areconstants, then Var(aX + bY + c) = a2 Var(X) + b2 Var(Y) (;N~ ~ 'i~~~~mes c. Never 3. The value of <1>(5.0) is ~ ~~~.ver nearlyO . Very near y c. Cannot e accurately determined 4. If X and Yare independent random variables with common standard deviation 0', then thestandard deviation of ~ X-! Y is 4 4 a. ~O' Vav- ct z ~-{~) Q]j;) -:.. (1 ) 2 V~-g:.) + (-t)-z.\1,t-~) C.O' f Q '2- '-a.. ..s- '2.. ::.J-CJ"~ -0- ::"_",",, CoO' I. r ~ v~:-(~~-=-i-;)- -=-JT ~ 2
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5. (18 pts.) The (total) ankle diameter of a sample of 507 adults is displayed in the histogram below. As you can see, it is reasonable to assume that ankle diameter is normally distributed. Suppose that a good-fitting normal curve to this data is one with a mean, ,Lt,of 13.90 cm, and a standard deviation, 0", of 1.25 cm. x: ::. /t,Jj(t...~ j? ~r;.1t;L. 0.3 0.2 U) c: Q) 0 0.1 0.0 10 11 12 13 14 15 16 17 18 Ankle Diameter (cm) Assume that the sample of 507 adultsis representative of the U.S. adult population as a
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