 127.1: The table at the right shows recent composite ACT scores. Determine...
 127.2: What percent would you expect to score between 19 and 23?
 127.3: What percent would you expect to score between 23 and 25?
 127.4: What is the probability that a student chosen at random scored betw...
 127.5: About how many batteries will last between 90,000 and 110,000 miles?
 127.6: About how many batteries will last more than 120,000 miles?
 127.7: About how many batteries will last less than 90,000 miles?
 127.8: What is the probability that if you buy a car battery at random, it...
 127.9: U.S. Population Age Percent 019 28.7 2039 29.3 4059 25.5 6079 13.3 ...
 127.10: Record High U.S. Temperatures Temperature (F) Number of States 1001...
 127.11: SCHOOL The frequency table at the right shows the gradepoint averag...
 127.12: About what percent of the males have cholesterol below 4.2?
 127.13: About how many of the 900 men in a study have cholesterol between 4...
 127.14: What percent of the time will you get more than 8 ounces of coffee?
 127.15: What percent of the time will you get less than 8 ounces of coffee?
 127.16: What percent of the time will you get between 7.4 and 8.6 ounces of...
 127.17: What percent of the CDs would you expect to be greater than 120 mil...
 127.18: If the company manufactures 1000 CDs per hour, how many of the CDs ...
 127.19: About how many CDs per hour will be too large to fit in the drives?
 127.20: About what percent of the products last between 150 and 210 days?
 127.21: About what percent of the products last between 180 and 210 days?
 127.22: About what percent of the products last less than 90 days?
 127.23: About what percent of the products last more than 210 days?
 127.24: Find the mean.
 127.25: Find the standard deviation.
 127.26: If the data are normally distributed, what percent of the time will...
 127.27: OPEN ENDED Sketch a positively skewed graph. Describe a situation i...
 127.28: CHALLENGE The graphing calculator screen shows the graph of a norma...
 127.29: Writing in Math Use the information on page 724 to explain how the ...
 127.30: ACT/SAT If x + y = 5 and xy = 6, what is the value of x 2 + y 2 ? A...
 127.31: REVIEW Jessica wants to create several different 7character passwo...
 127.32: {7, 16, 9, 4, 12, 3, 9, 4}
 127.33: {12, 14, 28, 19, 11, 7, 10}
 127.34: P(jack or queen)
 127.35: P(ace or heart)
 127.36: P(2 or face card)
 127.37: e4
 127.38: e3
 127.39: e  _1 2
Solutions for Chapter 127: The Normal Distribution
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 127: The Normal Distribution
Get Full SolutionsSince 39 problems in chapter 127: The Normal Distribution have been answered, more than 56164 students have viewed full stepbystep solutions from this chapter. Chapter 127: The Normal Distribution includes 39 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.