A Section 4.3 f Li www.webassign.net/web/Student/Assignment-Responses/last?dep=

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A Section 4.3 f Li www.webassign.net/web/Student/Assignment-Responses/last?dep= 13038881 :: Apps WebAssign Heinle Learning g Bookshelf Onlin D understanding-... , Section 4.4 Chegg.com evinhicksema renter-occupied housing distribution owner-occupied housing distribution Find the standard deviation for both distributions. The standard deviation provides a numerical measure of spread. (Round your answers to three decimal places.) owner-occupied housing renter-occupied housing 4. + -12 points MIntroStat6 4.E.080 My Notes Ask Your Teacher Role-playing games like Dungeons & Dragons use many different types of dice. Suppose that a four-sided die has faces marked 1, 2, 3, 4. The intelligence of a character is determined by rolling this die twice and adding 1 to the sum of the spots. The faces are equally likely and the two rolls are independent. What is the average (mean) intelligence for such characters? How spread out are their intelligences, as measured by the standard deviation of the distribution? (Round your answer to four decimal places.) 5. +-12 points MIntroStat6 4.E.081 My Notes Ask Your Teacher A mechanical assembly consists of a rod with a bearing on each end. The three parts are manufactured independently, and a vary a bit from part to part. The length of the rod has mean 10 centimeters (cm) and standard deviation 0.14 millimeters (mm). The length of a bearing has mean 3 cm and standard deviation 0.03 mm. What are the mean and standard deviation of the total length of the assembly? (Round your standard deviation answer to four decimal places.) cm Bearing Rod Bearing Submit Assignment Home My Assignments Extension Reques WebAssign® 4.01997-2016 Advanced Instructional Systems, Inc. All nghts reserved. Hula Grl.jpg product-64687 jpg Show all downloads... x Ask me anything 5:38 PM 2/29/2016

Explanation / Answer

4) Let X be the random variable (sum of the dice outputs +1). The probability distribution of X is given below,

Mean = Expectation = E(X) = (1/16) [3+4x2+5x3+6x4+7x3+8x2+9]

                                            = 96/16 =6

Variance = E(X2 )-E(X)2 = (1/16)[9+16x2+25x3+36x4+49x3+64x2+81]-36

                                       =4

So standard deviation =2

5)

Let X and Y represent the random variables corresponding to the rod and the beam.

We are interested in the random variable Z =X +2Y.

So mean Z = E(X+2Y) = E(X) + 2E(Y) = 16 cm

Variance (Z) = V(X+2Y) = V(X) + 4 V(Y) = 0.14+0.06 = 0.2 mm

So the standard deviation = 0.4472 mm

X 3 4 5 6 7 8 9 Prob(X) 1/16 2/16 3/16 4/16 3/16 2/16 1/16

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