1 Starting With Matlab 2 Creating Arrays 3 Mathematical Operations With Arrays 4 Using Script Files And Managing Data 5 Two-dimensional Plots 6 Programming In Matlab 7 User-defined Functions And Function Files 8 Polynomials, Curve Fitting, And Interpolation 9 Applications In Numerical Analysis 10 Three-dimensional Plots 11 Symbolic Math Chapter1: Starting With Matlab
Chapter Questions Section: Chapter Questions
Problem 1P Problem 2P: Calculate: (a) 8+802.6+e3.53 (b) 175)+733.131/4+550.41 Problem 3P: Calculate: (a) 23+453160.7+log10589006 (b) (36.12.25)(e2.3+20) Problem 4P: Calculate: (a) 3.822.754125+5.2+1.853.5 (b) 2.110615.21053610113 Problem 5P: Calculate: (a)sin0.2cos/6+tan72 (b) (tan64cos15)+sin237cos220 Problem 6P: Define the varialbe z as z = 4.5; than evaluate: (a) 0.44+3.1z2162.3z80.7 (b) z323/z2+17.53 Problem 7P: Define the variable t as t= 3.2; then evalute: (a) 12e2t3.81t3 (b) 6t2+6t2t21 Problem 8P: Define the variable xandy as x = 6.5 and y = 3.8; then evaluate: (a) x2+y22/3+xyyx (b) x+yxy2+2x2xy2 Problem 9P: Define the variables a, b, c, and d as: c= 4.6, d = 1.7, a = cd2, and b=c+acd; then evaluate: (a)... Problem 10P: Two trigonometric identities are given by: (a) cos2xsin2x=12sin2x (b) tanxsinx2tanx=1cosx2 For each... Problem 11P: Two trigonometric identities are given by: (a) sinx+cosx2=1+2sinxcosx (b)... Problem 12P: Define two variables: alpha =8, and beta = 6. Using these variables, show that the following... Problem 13P: Given: x2cosxdx=2xcosx+x22sinx . Use MATLAB to calculaet the following difinite integral:... Problem 14P: A rectangular box has the dimensions shown. (a) Determine the angle BAC to the nearest degree. (b)... Problem 15P: The are length of a segment of a parabola ABC is given by: LABC=a2+4h2+2ha+2ha2+1 Determine LABC if... Problem 16P: The three shown circles, with radius 15 in., 10.5 in., and 4.5 in., are tangent to each other. (a)... Problem 17P: A frustum of cone is filled with ice cream such that the portion above the cone is a hemisphere.... Problem 18P: 18. In the triangle shown a =27 in., b 43 in., c=57 in. Define a, b, and c as variables, and then:... Problem 19P: For the triangle shown, a = 72°, ß=43°, and its perimeter is p = 114 mm. Define a, ß, and p, as... Problem 20P: The distance d from a point P (xp,yp,zp) to the line that passes through the two points A (xA,yA,zA)... Problem 21P: The perimeter of an ellipse can be approximated by: P=(a+b)3(3a+b)(a+3b)a+b Calculate the perimeter... Problem 22P: A total of 4217 eggs have w be packed in boxes that can hold 36 eggs each. By typing one line... Problem 23P: A total of 777 people have to be transported using buses that have 46 seats and vans that have 12... Problem 24P: Change the display to format long g. Assign the number 7E8/13 to a variable, and then use the... Problem 25P: The voltage difference Vabbetween points a and b in the Wheatstone bride circuit is given by:... Problem 26P: The current in a series RCL circuit is given by: I=VR2(L1C)2 Where =2 f. Calculate I for the... Problem 27P: The monthly payment M of a mortgage P for n years with a fixed annual interest rate r can be... Problem 28P: The number of permutations nProf taking r Objects out of n objects without repetition is given by:... Problem 29P: The number of combinations Cn,r of taking r objects out of n objects is given by: aye In the... Problem 30P: The equivalent resistance of two resistors R1and R2connected in parallel is given by Req=R1R2R1+R2 .... Problem 31P: The output voltage Voutin the circuit shown is given by (Millman’s theorem):... Problem 32P: Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is... Problem 33P: The greatest common divisor is the largest positive integer that divides the numbers without a... Problem 34P: The amount of energy E (in joules) that is released by an earthquake is given by: E=1.741019101.44M... Problem 35P: According to the Doppler effect of light, the perceived wavelength ?p, of a light source with a... Problem 36P: Newton’s law of cooling gives the temperature T(t) of an object at time tin terms of T0, its... Problem 37P: The velocity v and the falling distance d as a function of time of a skydiver that experience the... Problem 38P: Use the Help Window to find a display format that displays the output as a ratio of integers. For... Problem 39P: Gosper’s approximation for factorials is given by: n!=2n+13nnen Use the formula for calculating 19!.... Problem 40P: According to Newton’s law of universal gravitation, the attraction force between two bodies is given... Problem 1P
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Assume that Z is a number randomly chosen from a standard normal distribution . Use the standard normal table to calculate each of the following probabilities:
a. Pr[Z>1.34] b. Pr[Z<1.34] c. Pr[Z>2.15] d. Pr[Z<1.2] e. Pr[0.52<Z<2.34] f. Pr[-2.34<Z<-0.52] g. Pr[Z<-0.93] h. Pr[Z>-0.93] i. Pr-1.57<Z<-0.32]
Transcribed Image Text: The image displays a detailed z-table, also known as a standard normal distribution table. This table provides the cumulative probability of a standard normal random variable, typically used in statistics for finding the probability that a statistic is observed below, at, or above a standard score (z-score).
### Table Explanation:
- **Columns and Rows**: The table is organized with z-scores along the rows and additional decimal values in the columns.
- **Z-Scores**:
- The first column on the left represents the whole number and first decimal of the z-score.
- The remaining columns represent the second decimal place of the z-score.
- **Entries**: Each cell within the table shows the probability that a statistic is less than the corresponding z-score. For example, if the z-score is 1.6, the probability is 0.9452.
- **Usage**: To find the cumulative probability of a z-score:
1. Locate the first digit and the first decimal in the row (y-axis).
2. Find the second decimal in the top row (x-axis).
3. The point where the row and column intersect gives the probability.
This table is essential for statistical calculations, especially when working with data that follows a normal distribution pattern. It's commonly used in hypothesis testing, confidence intervals, and other statistical inferences.
Note that the table provided covers z-scores from 1.6 to 4.0, useful for relatively high values, indicating the tail ends of a standard normal distribution.
Transcribed Image Text: The image displays a statistical table used to calculate standard normal distribution probabilities. The heading indicates it applies the formula: `1 - NORM.DIST(1.96, 0, 1, TRUE)`, which relates to the cumulative distribution function for the standard normal distribution.
### Table Breakdown:
- **Rows and Columns**: The table has rows labeled by the first two digits after the decimal (a.bc), ranging from 0.0 to 1.9. The columns, labeled by the second digit after the decimal (c), range from 0 to 9.
- **Purpose**: This table provides probabilities for the standard normal distribution (Z-scores) rounded to two decimal places. For example, if you are looking up a Z-score of 0.45, you first go to the row labeled 0.4 and then move to the column labeled 5. The value at this intersection gives the cumulative probability from the mean.
### Using the Table:
1. **Locate the First Two Digits**: Find the row corresponding to the first two digits of the Z-score.
2. **Find the Second Decimal Place**: Move across the row to the column representing the second decimal place.
3. **Read the Probability**: The cell value is the cumulative probability for that Z-score.
### Example:
- To find the cumulative probability for Z = 0.45:
- Check row 0.4 and then column 5.
- The value is 0.32636.
This table is an essential tool for statistical analysis in fields such as psychology, finance, and any domain requiring normal distribution probabilities. It aids in determining the probability of a value falling below a particular Z-score in a standard normal distribution.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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