A government bureau collects and reports information about naturalized persons i
ID: 3059811 • Letter: A
Question
A government bureau collects and reports information about naturalized persons in their statistical database. The accompanying data table shows the age distribution for persons naturalized during one year. Suppose that one of these naturalized persons is selected at random.
1. Without using the general addition rule, determine the probability that the age of the person obtained is either between 35 and 59, inclusive, or at least 50.
How can the probability be computed without using the general addition rule?
2. Identify the probability of the event without using the general addition rule. The probability that the age of the person obtained is either between 35 and 59, inclusive, or at least 50 is?
(Type an integer or a decimal. Round to three decimal places as needed.)
3. Find the probability in part (a), using the general addition rule. Identify the three probabilities used in the general addition rule.
The probability that the age of the person obtained is between 35 and 59, inclusive, is ?
The probability that the age of the person obtained is at least 50 is ?
The probability that the age of the person obtained is between 35 and 59, inclusive, and at least 50, is ?
(Type integers or decimals. Round to three decimal places as needed.)
4. Identify the probability of the event using the general addition rule.
Using the general addition rule, the probability that the age of the person obtained is either between 35 and 59, inclusive, or at least 50 is ?
(Type an integer or a decimal. Round to three decimal places as needed.)
Age Frequency Age Frequency 18-19 6192 45-49 42763 20-24 50393 50-54 33530 25-29 59767 55-59 22931 30-34 66742 59-64 18811 35-39 67109 65-74 22579 40-44 55310 75 and up 7628Explanation / Answer
1:
using complement rule:
P(between 35 and 50 or at least 50)= 1- P(less than 35)
2:
Following table shows the total number of persons and cumulative frequencies:
The total number of persons is : 453755
Out of these 453755, 183094 are less than 35 so the probability that the age of the person obtained is either between 35 and 59, inclusive, or at least 50 is
P(between 35 and 50 or at least 50)= 1- P(less than 35) = 1 - (183094 / 453755 ) = 0.596
3:
The probability that the age of the person obtained is between 35 and 59, inclusive, is
P(between 35 and 59) = 221643 /453755 = 0.488
The probability that the age of the person obtained is at least 50 is
P(at least 50) = 105479 /453755 = 0.232
The probability that the age of the person obtained is between 35 and 59, inclusive, and at least 50, is
P(between 35 and 59, inclusive, and at least 50) = 56461 /453755 = 0.124
4:
Using the general addition rule, the probability that the age of the person obtained is either between 35 and 59, inclusive, or at least 50 is
P(between 35 and 50 or at least 50) = P(between 35 and 59)+P(at least 50) -P(between 35 and 59, inclusive, and at least 50) = 0.488+0.232-0.124 = 0.596
Age Frequency Cumuative freqeuncy 18-19 6192 6192 20-24 50393 56585 25-29 59767 116352 30-34 66742 183094 35-39 67109 250203 40-44 55310 305513 45-49 42763 348276 50-54 33530 381806 55-59 22931 404737 59-64 18811 423548 65-74 22579 446127 75 and up 7628 453755 Total 453755