Superlesson
Project 1-2
Advanced Algebra
Chapter 1, Mathematical Models
Each day several thousand fireballs--very bright meteors--streak through the earth's atmosphere. A few strike the earth's surface. Because observations and landings of fireballs occur at random locations, they can be analyzed using probabilities.
Part A, Theoretical and Experimental Probability
1. The American Meteor Society keeps track of meteor sightings. How likely are they to occur at any given time?
a. What is the theoretical probability that a fireball observed in March will occur on March 29? What is the experimental probability that a March 1998 fireball reported to the American Meteor Society was observed on March 29?
b. What is the theoretical probability that a fireball will occur between the hours of 6 p.m. (1800) and 6 a.m. (0600) local time? What is the experimental probability that a March 1998 fireball reported to the American Meteor Society occurred between the hours of 6 p.m and 6 a.m. local time?
c. Explain the discrepancy in question b.
d. Refer to "Frequently Asked Questions" (FAQs) about fireballs. If you find a meteorite, what is the probability that it will belong to the iron class? (See FAQ 13.)
e. What is the probability that a meteorite fall (landing) will occur over an ocean or uninhabited land area? (See FAQ 10.)
f. Use the data in FAQ 10 to estimate the surface area of the earth in square miles. (Use the average of the given numbers of daily "meteorite dropping events.") Explain how you got your answer.
Part B, Simulation
2. Meteors come from comets and asteroids.
a. What percentage of all Meteors have their origins in asteroids? (See FAQ 7.)
b. Describe how you can take digits in a list of random numbers in pairs to represent meteors with their origins in asteroids and meteors with their origins in comets. Use these random digits to illustrate your method: 7, 3, 3, 4, 0, 9, 1, 9, 0, 2
c. Suppose 10 meteorites fall to earth each day. (The actual number ranges from about 10 to about 50 daily.) Use the following random digits to simulate meteorite falls over 10 days. What is the probability that two or more meteorites with their origins in asteroids will fall to earth in a day?
55031 98877 01475 66477 01013 27614 66513 70555 26304 64800 50863 36410 21830 07694 69346 44580 23183 41827 88575 30166 84622 39089 36083 45246 42488 78077 69882 61657 34136 79180 97526 04098 32906 07408 11977 09013 23982 25835 14367 24010
Part C, Making Connections
3. A meteorite struck the earth somewhere in Colorado.
a. What is the probability that it landed in Montrose County? To obtain the information you'll need, open the U.S. map Web site. Scroll to the bottom and click on Colorado.
Hint: To find data on Colorado, look at the top of the page and click on the words State of Colorado. Open the Summary Report and select "Land Area." Then click on "Get the above Selected report." The land area data will appear an the bottom of the screen. Record the data.
To find Montrose County data, go back to the Colorado Counties map and click on "Montrose County." Repeat the steps above to find the land area.