 13.6.13.1.185: A distribution in which all the values have the same frequency is c...
 13.6.13.1.186: A distribution in which the frequency is either constantly increasi...
 13.6.13.1.187: A distribution that has a tail on its right is skewed to the .
 13.6.13.1.188: A distribution that has a tail on its left is skewed to the .
 13.6.13.1.189: A distribution in which two nonadjacent values occur more frequentl...
 13.6.13.1.190: A normal distribution is a(n) shaped distribution.
 13.6.13.1.191: A measure of how far, in terms of standard deviations, a given data...
 13.6.13.1.192: The mean of a set of data will always have a zscore of
 13.6.13.1.193: A piece of data that has a negative zscore is the mean
 13.6.13.1.194: A piece of data that has a positive zscore is the mean.
 13.6.13.1.195: According to the empirical rule, in a normal distribution, a) appro...
 13.6.13.1.196: In a normal distribution, the mean, median, and mode all have the s...
 13.6.13.1.197: In Exercises 1316, give an example of the type of distribution. Rec...
 13.6.13.1.198: In Exercises 1316, give an example of the type of distribution. Skewed
 13.6.13.1.199: In Exercises 1316, give an example of the type of distribution.. J...
 13.6.13.1.200: In Exercises 1316, give an example of the type of distribution. Bim...
 13.6.13.1.201: For the distributions in Exercises 1720, state whether you think th...
 13.6.13.1.202: For the distributions in Exercises 1720, state whether you think th...
 13.6.13.1.203: For the distributions in Exercises 1720, state whether you think th...
 13.6.13.1.204: For the distributions in Exercises 1720, state whether you think th...
 13.6.13.1.205: Above the mean
 13.6.13.1.206: Below the mean
 13.6.13.1.207: Between two standard deviations below the mean and one standard dev...
 13.6.13.1.208: Between 1.10 and 1.60 standard deviations above the mean
 13.6.13.1.209: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.210: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.211: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.212: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.213: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.214: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.215: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.216: In Exercises 2132, use Table 13.7 on pages 822 and 823 to find the ...
 13.6.13.1.217: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.218: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.219: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.220: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.221: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.222: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.223: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.224: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.225: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.226: In Exercises 33 42, use Table 13.7 on pages 822 and 823 to determin...
 13.6.13.1.227: Heights of Girls In Exercises 43 and 44, assume that the heights of...
 13.6.13.1.228: Heights of Girls In Exercises 43 and 44, assume that the heights of...
 13.6.13.1.229: Police Officers Salaries In Exercises 45 48, assume the annual sala...
 13.6.13.1.230: Police Officers Salaries In Exercises 45 48, assume the annual sala...
 13.6.13.1.231: Police Officers Salaries In Exercises 45 48, assume the annual sala...
 13.6.13.1.232: Police Officers Salaries In Exercises 45 48, assume the annual sala...
 13.6.13.1.233: SAT Scores In Exercises 49 54, assume that the mathematics scores o...
 13.6.13.1.234: SAT Scores In Exercises 49 54, assume that the mathematics scores o...
 13.6.13.1.235: SAT Scores In Exercises 49 54, assume that the mathematics scores o...
 13.6.13.1.236: SAT Scores In Exercises 49 54, assume that the mathematics scores o...
 13.6.13.1.237: SAT Scores In Exercises 49 54, assume that the mathematics scores o...
 13.6.13.1.238: SAT Scores In Exercises 49 54, assume that the mathematics scores o...
 13.6.13.1.239: Vending Machine In Exercises 5558, a vending machine is designed to...
 13.6.13.1.240: Vending Machine In Exercises 5558, a vending machine is designed to...
 13.6.13.1.241: Vending Machine In Exercises 5558, a vending machine is designed to...
 13.6.13.1.242: Vending Machine In Exercises 5558, a vending machine is designed to...
 13.6.13.1.243: Automobile Speed In Exercises 59 64, assume that the speed of autom...
 13.6.13.1.244: Automobile Speed In Exercises 59 64, assume that the speed of autom...
 13.6.13.1.245: Automobile Speed In Exercises 59 64, assume that the speed of autom...
 13.6.13.1.246: Automobile Speed In Exercises 59 64, assume that the speed of autom...
 13.6.13.1.247: Automobile Speed In Exercises 59 64, assume that the speed of autom...
 13.6.13.1.248: Automobile Speed In Exercises 59 64, assume that the speed of autom...
 13.6.13.1.249: Corn Flakes In Exercises 65 68, assume that the amount of corn flak...
 13.6.13.1.250: Corn Flakes In Exercises 65 68, assume that the amount of corn flak...
 13.6.13.1.251: Corn Flakes In Exercises 65 68, assume that the amount of corn flak...
 13.6.13.1.252: Corn Flakes In Exercises 65 68, assume that the amount of corn flak...
 13.6.13.1.253: Cost of Day Care In Exercises 6974, assume the annual day care cost...
 13.6.13.1.254: Cost of Day Care In Exercises 6974, assume the annual day care cost...
 13.6.13.1.255: Cost of Day Care In Exercises 6974, assume the annual day care cost...
 13.6.13.1.256: Cost of Day Care In Exercises 6974, assume the annual day care cost...
 13.6.13.1.257: Cost of Day Care In Exercises 6974, assume the annual day care cost...
 13.6.13.1.258: Cost of Day Care In Exercises 6974, assume the annual day care cost...
 13.6.13.1.259: Weight Loss A weightloss clinic guarantees that its new customers ...
 13.6.13.1.260: Battery Warranty The warranty on a car battery is 36 months. If the...
 13.6.13.1.261: Coffee Machine A vending machine that dispenses coffee does not app...
 13.6.13.1.262: Grading on a Normal Curve Mr. Sanderson marks his class on a normal...
 13.6.13.1.263: Consider the following normal curve, representing a normal distribu...
 13.6.13.1.264: Consider the following two normal curves. 28 30 32 34 36 38 40 42 4...
 13.6.13.1.265: In a distribution that is skewed to the right, which has the greate...
 13.6.13.1.266: In a distribution skewed to the left, which has the greatest value:...
 13.6.13.1.267: List three populations other than those given in the text that may ...
 13.6.13.1.268: List three populations other than those given in the text that may ...
 13.6.13.1.269: Salesperson Promotion The owner at Kims Home Interiors is reviewing...
 13.6.13.1.270: Chebyshevs Theorem How can you determine whether a distribution is ...
 13.6.13.1.271: Test Scores Obtain a set of test scores from your instructor. a) De...
 13.6.13.1.272: Determine a value of z such that z 0 and 47.5% of the standard norm...
 13.6.13.1.273: Determine a value of z such that z 0 and 38.1% of the standard norm...
 13.6.13.1.274: Ask your instructor for the class mean and class standard deviation...
 13.6.13.1.275: If the mean score on a math quiz is 12.0 and 77% of the students in...
 13.6.13.1.276: In this project, you actually become the statistician. a) Select a ...
Solutions for Chapter 13.6: Statistics
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 13.6: Statistics
Get Full SolutionsChapter 13.6: Statistics includes 92 full stepbystep solutions. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. Since 92 problems in chapter 13.6: Statistics have been answered, more than 79466 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Outer product uv T
= column times row = rank one matrix.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.