Murder Victims. As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table. Age (yr) Frequency 20–24 2329 25–29 1892 30–34 1414 35–39 1046 40–44 900 45–49 854 50–54 673 55–59 500 A murder case in which the person murdered was between 20 and 59 years old is selected at random. Find the probability that the murder victim wasa. between 40 and 44 years old, inclusive.b. at least 25 years old, that is, 25 years old or older.c. between 45 and 59 years old, inclusive.d. under 30 or over 54.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Murder Victims. As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table.
|
Age (yr) |
Frequency |
|
20–24 |
2329 |
|
25–29 |
1892 |
|
30–34 |
1414 |
|
35–39 |
1046 |
|
40–44 |
900 |
|
45–49 |
854 |
|
50–54 |
673 |
|
55–59
|
500
|
A murder case in which the person murdered was between 20 and 59 years old is selected at random. Find the probability that the murder victim was
a. between 40 and 44 years old, inclusive.
b. at least 25 years old, that is, 25 years old or older.
c. between 45 and 59 years old, inclusive.
d. under 30 or over 54.
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