Finite Mathematics and Calculus with Applications (10th Edition)
10th Edition
ISBN: 9780321979407
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Textbook Question
Chapter 18.2, Problem 43E
Time of Traffic Fatality In Exercise 51 of the previous section, the probability density function for the number of fatal traffic accidents was found to be
where t is the number of hours since midnight on [0, 24]. Calculate the expected time of day at which a fatal accident will occur. Source: The National Highway Traffic Safety Administration.
51. Time of Traffic Fatality The National Highway Traffic Safety Administration records the time of day of fatal crashes. The table on the next page gives the time of day (in hours since midnight) and the frequency of fatal crashes in 2012. Source: The National Highway Traffic Safety Administration.
(a) Plot the data. What type of function appears to best match these data?
(b) Use the regression feature on your graphing calculator to find a cubic equation that models the time of day, t, and the number of traffic fatalities, T(t). Use the midpoint value to estimate the time in each interval. Graph the function with the plot of the data. Does the graph fit the data?
| Time of Day | Midpoint of Interval (hours) | Frequency |
| 0–3 | 1.5 | 3817 |
| 3–6 | 4.5 | 2560 |
| 6–9 | 7.5 | 2950 |
| 9–12 | 10.5 | 2982 |
| 12–15 | 13.5 | 3973 |
| 15–18 | 16.5 | 4964 |
| 18–21 | 19.5 | 5003 |
| 21–24 | 22.5 | 4310 |
| Total | 30,559 |
(c) By finding an appropriate constant k, find a function S(t) – kT(t) that is a probability density function describing the probability of a traffic fatality at a particular time of day.
(d) For a randomly chosen traffic fatality, find the probabilities that the accident occurred between 12 A.M. and 2 A.M. (t = 0 to t = 2) and between 4 P.M. and 5:30 P.M. (t = 16 to t = 17.5).
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Chapter 18 Solutions
Finite Mathematics and Calculus with Applications (10th Edition)
Ch. 18.1 - Prob. 1YTCh. 18.1 - Prob. 2YTCh. 18.1 - Using the probability density function of Example...Ch. 18.1 - Use part (a) of Example 5 to calculate the...Ch. 18.1 - Evaluate each of the following integrals. (Sec....Ch. 18.1 - Prob. 2WECh. 18.1 - Prob. 3WECh. 18.1 - Decide whether the functions defined as follows...Ch. 18.1 - Prob. 2ECh. 18.1 - Prob. 3E
Ch. 18.1 - Prob. 4ECh. 18.1 - Prob. 5ECh. 18.1 - Prob. 6ECh. 18.1 - Prob. 7ECh. 18.1 - Prob. 8ECh. 18.1 - Prob. 9ECh. 18.1 - Prob. 10ECh. 18.1 - Prob. 11ECh. 18.1 - Prob. 12ECh. 18.1 - Prob. 13ECh. 18.1 - Prob. 14ECh. 18.1 - Prob. 15ECh. 18.1 - Prob. 16ECh. 18.1 - Prob. 17ECh. 18.1 - Prob. 18ECh. 18.1 - Prob. 19ECh. 18.1 - Prob. 20ECh. 18.1 - Prob. 21ECh. 18.1 - Find the cumulative distribution function for the...Ch. 18.1 - Prob. 23ECh. 18.1 - Prob. 24ECh. 18.1 - Prob. 25ECh. 18.1 - Prob. 26ECh. 18.1 - Prob. 27ECh. 18.1 - Prob. 28ECh. 18.1 - Prob. 29ECh. 18.1 - Prob. 30ECh. 18.1 - Prob. 31ECh. 18.1 - Prob. 32ECh. 18.1 - Prob. 33ECh. 18.1 - Prob. 34ECh. 18.1 - Life Span of a Computer Part The life (in months)...Ch. 18.1 - Prob. 36ECh. 18.1 - Prob. 37ECh. 18.1 - Prob. 38ECh. 18.1 - Prob. 39ECh. 18.1 - Prob. 40ECh. 18.1 - Prob. 41ECh. 18.1 - Flea Beetles The mobility of an insect is an...Ch. 18.1 - Prob. 43ECh. 18.1 - Prob. 44ECh. 18.1 - Prob. 45ECh. 18.1 - Earthquakes The time between major earthquakes in...Ch. 18.1 - Earthquakes The time between major earthquakes in...Ch. 18.1 - Prob. 48ECh. 18.1 - Driving Fatalities We saw in a review exercise in...Ch. 18.1 - Prob. 50ECh. 18.1 - Time of Traffic Fatality The National Highway...Ch. 18.2 - Repeat Example l for the probability density...Ch. 18.2 - Prob. 2YTCh. 18.2 - Prob. 3YTCh. 18.2 - Find P(1 X 2) for each probability function on...Ch. 18.2 - Prob. 2WECh. 18.2 - Prob. 1ECh. 18.2 - Prob. 2ECh. 18.2 - Prob. 3ECh. 18.2 - Prob. 4ECh. 18.2 - Prob. 5ECh. 18.2 - Prob. 6ECh. 18.2 - Prob. 7ECh. 18.2 - In Exercises 18, a probability density function of...Ch. 18.2 - Prob. 9ECh. 18.2 - Prob. 10ECh. 18.2 - Prob. 11ECh. 18.2 - Prob. 12ECh. 18.2 - Prob. 13ECh. 18.2 - Prob. 14ECh. 18.2 - Prob. 15ECh. 18.2 - Prob. 16ECh. 18.2 - Prob. 17ECh. 18.2 - For Exercises 1520, (a) find the median of the...Ch. 18.2 - Prob. 19ECh. 18.2 - Prob. 20ECh. 18.2 - Prob. 21ECh. 18.2 - Prob. 22ECh. 18.2 - Prob. 23ECh. 18.2 - Prob. 24ECh. 18.2 - Prob. 25ECh. 18.2 - Prob. 26ECh. 18.2 - Losses After Deductible A manufacturers annual...Ch. 18.2 - Prob. 28ECh. 18.2 - Prob. 29ECh. 18.2 - Prob. 30ECh. 18.2 - Prob. 31ECh. 18.2 - Prob. 32ECh. 18.2 - Petal Length The length (in centimeters) of a...Ch. 18.2 - Prob. 34ECh. 18.2 - Prob. 35ECh. 18.2 - Prob. 36ECh. 18.2 - Prob. 37ECh. 18.2 - Prob. 38ECh. 18.2 - Annual Rainfall The annual rainfall in a remote...Ch. 18.2 - Prob. 40ECh. 18.2 - Prob. 41ECh. 18.2 - Prob. 42ECh. 18.2 - Time of Traffic Fatality In Exercise 51 of the...Ch. 18.3 - Prob. 1YTCh. 18.3 - Prob. 2YTCh. 18.3 - Prob. 3YTCh. 18.3 - Prob. 1WECh. 18.3 - Prob. 2WECh. 18.3 - Prob. 1ECh. 18.3 - Prob. 2ECh. 18.3 - Find (a) the mean of the distribution, (b) the...Ch. 18.3 - Prob. 4ECh. 18.3 - Prob. 5ECh. 18.3 - Prob. 6ECh. 18.3 - Prob. 7ECh. 18.3 - Prob. 8ECh. 18.3 - Prob. 9ECh. 18.3 - Prob. 10ECh. 18.3 - Prob. 11ECh. 18.3 - Prob. 12ECh. 18.3 - Prob. 13ECh. 18.3 - Prob. 14ECh. 18.3 - Prob. 15ECh. 18.3 - Prob. 16ECh. 18.3 - Prob. 17ECh. 18.3 - Prob. 18ECh. 18.3 - Prob. 19ECh. 18.3 - Prob. 20ECh. 18.3 - Prob. 21ECh. 18.3 - Prob. 22ECh. 18.3 - Prob. 23ECh. 18.3 - Prob. 24ECh. 18.3 - Prob. 25ECh. 18.3 - Prob. 26ECh. 18.3 - Prob. 27ECh. 18.3 - Prob. 28ECh. 18.3 - Prob. 29ECh. 18.3 - Prob. 30ECh. 18.3 - Prob. 31ECh. 18.3 - Prob. 32ECh. 18.3 - Prob. 33ECh. 18.3 - Prob. 34ECh. 18.3 - Insured Loss An insurance policy is written to...Ch. 18.3 - Prob. 36ECh. 18.3 - Printer Failure The lifetime of a printer costing...Ch. 18.3 - Prob. 38ECh. 18.3 - Prob. 39ECh. 18.3 - Prob. 40ECh. 18.3 - Prob. 41ECh. 18.3 - Prob. 42ECh. 18.3 - Finding Prey H. R. Pulliam found that the time (in...Ch. 18.3 - Life Expectancy According to the National Center...Ch. 18.3 - Prob. 45ECh. 18.3 - Prob. 46ECh. 18.3 - Prob. 47ECh. 18.3 - Prob. 48ECh. 18.3 - Prob. 49ECh. 18.3 - Prob. 50ECh. 18.3 - Prob. 51ECh. 18.3 - Prob. 52ECh. 18.3 - Prob. 53ECh. 18.3 - Prob. 54ECh. 18 - Prob. 1RECh. 18 - Prob. 2RECh. 18 - Prob. 3RECh. 18 - Prob. 4RECh. 18 - Prob. 5RECh. 18 - Prob. 6RECh. 18 - Prob. 7RECh. 18 - Prob. 8RECh. 18 - Prob. 9RECh. 18 - Prob. 10RECh. 18 - Prob. 11RECh. 18 - Prob. 12RECh. 18 - Prob. 13RECh. 18 - Prob. 14RECh. 18 - Prob. 15RECh. 18 - Prob. 16RECh. 18 - Prob. 17RECh. 18 - Prob. 18RECh. 18 - Prob. 19RECh. 18 - Prob. 20RECh. 18 - Prob. 21RECh. 18 - Prob. 22RECh. 18 - Prob. 23RECh. 18 - Prob. 24RECh. 18 - Prob. 25RECh. 18 - Prob. 26RECh. 18 - Prob. 27RECh. 18 - Prob. 28RECh. 18 - Prob. 29RECh. 18 - Prob. 30RECh. 18 - Prob. 31RECh. 18 - Prob. 32RECh. 18 - Prob. 33RECh. 18 - Prob. 34RECh. 18 - Prob. 35RECh. 18 - Prob. 36RECh. 18 - Prob. 37RECh. 18 - Prob. 38RECh. 18 - Prob. 39RECh. 18 - Prob. 40RECh. 18 - Prob. 41RECh. 18 - Prob. 42RECh. 18 - Prob. 43RECh. 18 - Prob. 44RECh. 18 - Prob. 45RECh. 18 - Prob. 46RECh. 18 - Prob. 47RECh. 18 - Prob. 48RECh. 18 - Prob. 49RECh. 18 - Prob. 50RECh. 18 - Prob. 51RECh. 18 - Prob. 52RECh. 18 - Prob. 53RECh. 18 - Prob. 54RECh. 18 - Prob. 55RECh. 18 - Prob. 56RECh. 18 - Prob. 57RECh. 18 - Prob. 58RECh. 18 - Prob. 59RECh. 18 - Prob. 60RECh. 18 - Prob. 61RECh. 18 - Prob. 62RE
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