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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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| 364 58% I 08:01 Answered: i. The data below sho C i. The data below shows the maximum temperature ("C) and the number of bowls of soup sold at God's Grace Canteen on eleven randomly selected days last year. Day 1 2 3 4 5| 6|7 10 11 8 9 Temp. (C) 32 36 22 29 25 18 11 16 5 2 Bowls Sold 10 10 20 35 45 50 50 57 63 On graph paper, draw a scatter plot of temperature against bowls i. sold to represent the data using a scale of 1 cm to represent 5 bowls and 2cm to represent 5"C. ii. Write down the type of relationship between the variables. iii. Calculate the mean number of bowls of soup, x, sold. iv. Find the mean maximum temperature, y of soup recorded. Plot and label the point M (x, y ) on your graph. V. vi. The line of best fit for the data passes through the point M and the y- intercept (0, 33.2). Draw this line on your graph. vii. Find the equation of the line of best fit. vii. On another day of the year, the temperature was 20°C. Using the equation of the line of best fit, estimate…
1. There is a theory that people who drink caffeine can run longer than those who do not. To test this theory a random sample of seven people who drink caffeine and a random sample of seven people who do not drink caffeine was obtained and their length of time they could run non-stop was measured, in seconds. Non-Caffeine drinkers 359 280 138 227 203 184 231 Caffeine drinkers 394 477 439 428 391 488 454 a. At the 5% significance level, can you conclude that those who drink caffeine can run longer than those who do not? b. Are the samples independent or dependent? c. If independent, would using dependent samples have been better? Why or Why not? If depen- dent, explain why dependent samples were used.
1 Four salesmen were posted in different areas by a company. The number of units of commodity X sold by them are as follows: A 20 23 28 29 B 25 32 30 21 C 23 28 35 18 D 15 21 19 25 Test the hypothesis at 5% level that the average sales are equal.
Q.5. Strengths measured in tests on 26 building elements are given below arranged in the increasing order: I1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 | 19 | 20 21 22 23 24 25 26 X 69.571.972.673.1 73.373.5 74.1 74.275.3 75.5 75.775.8 76.176.2 76.2/76.9/77.0 77.9 78.179.6/79.779.9 80.1 82.283.7 93.7| Test the hypothesis that strength is normally distributed with following tests: a) * (Chi-Square) test at 10% level of significance (with 5 class intervals of equal probability) K-S (Kolmogorov-Smirnov) test at 10% level of significance. 2.
The accompanying data came from a study of collusion in bidding within the construction industry. No. Bidders No. Contracts 2 3 4 5 6 7 8 9 10 11 USE SALT 8 20 26 18 12 8 6 7 4 3 (a) What proportion of the contracts involved at most five bidders? At least five bidders? (Round your answers to four decimal places.) at most five bidders. at least five bidders X X (b) What proportion of the contracts involved between five and 10 bidders, inclusive? Strictly between five and 10 bidders? (Round your answers to four decimal places.) between five and 10 bidders, inclusive strictly between five and 10 bidders X X
Identify the maximum value, minimum value, median (Q2), first quartile (Q1), third quartile (Q3), and interquartile range (IQR) from the given boxplot. See Example 4. + + + 3 4 5 678 9 10 11 12 13 14 15 16 17 18 19 20 + Median (Q2): First Quartile Third Quartile (Q3): | Interquartile Range (IOR):
b) The following incomplete y versus x data is given. 2 4. 7 6. ??? 15 5 11 2?? 32 The data is fit by quadratic spline interpolants given by ax -1, -2x? + 14x – 9, 1sxs2 f(x) = bx2 + cx + d, 25x2-303x + 928, 6SxS7 Determine the missing entries in the table and the coefficients, a, b. c, and d of these quadratic splines.
EXAMPLE 3.20 Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data: Uses cell phone while driving Does not use cell phone while driving Total Table 3.2 Speeding violation in the last year 25 45 70 No speeding violation in the last year 280 405 685 Total Problem a. Find P(Driver is a cell phone user). b. Find P(Driver had no violation in the last year). c. Find P(Driver had no violation in the last year was a cell phone user). d. Find P(Driver is a cell phone user U driver had no violation in the last year). e. Find P(Driver is a cell phone user driver had a violation in the last year). 1. Find P(Driver had no violation last year driver was not a cell phone user) 305 450 *** 755 The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 +685 755. Calculate the following probabilities using the table.
1- Fit a least-square geometric curve y - ax to the following data 2 3 4 5 y 27.8 62.1 110 161
8. A histogram is better for _____________ data and a frequency polygon is better for ________data. a. discrete data, continuous data b. continuous data, discrete data c. neither a or b are correct d. both a and b are correct 12. A platykurtic has a _____kurtosis value, a mesokurtic has a _____ kurtosis value, and a leptokurtic has a ____ kurtosis value.

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