A study conducted by the Metro Housing Agency in a midwestern city revealed the information below concerning the age distribution of renters in the city. (Round your answers to four decimal places.)
Age Adult Population, % Group Who Are Renters, %
21-44 53 64
45-64 29 43
65 and over 18 62
(a) What is the probability that an adult selected at random from this population is a renter?
1
(b) If a renter is selected at random, what is the probability that he or she is in the 21-44 age bracket?
2
(c) If a renter is selected at random, what is the probability that he or she is 45 yr of age or older?
Confused by your third category of "%". % of what? It is not of the total number, since .64 + .43 + 62 ≠ 1.
Repost with data expressed more accurately.
the question is posted correctly. the question only gives percentages and nothing else.
To find the probability, we can use the formula:
Probability = Number of Successful Outcomes / Total Number of Outcomes
(a) The probability that an adult selected at random from this population is a renter can be found by adding up the percentages of renters from each age group and then dividing by the total number of age groups:
Probability = (64/100) + (43/100) + (62/100) = 0.64 + 0.43 + 0.62
Probability = 1.69
Therefore, the probability that an adult selected at random from this population is a renter is 1.69.
(b) To find the probability that a renter selected at random is in the 21-44 age bracket, we need to consider the percentage of renters in the 21-44 age bracket and divide it by the total percentage of renters:
Probability = (64/100) / (64/100 + 43/100 + 62/100)
Probability = (64/100) / (1.69)
Probability = 0.3787
Therefore, the probability that a renter selected at random is in the 21-44 age bracket is 0.3787.
(c) To find the probability that a renter selected at random is 45 years of age or older, we need to consider the percentage of renters in the 45-64 age group and the percentage of renters who are 65 and over, and then divide it by the total percentage of renters:
Probability = (43/100 + 62/100) / (64/100 + 43/100 + 62/100)
Probability = (43/100 + 62/100) / (1.69)
Probability = 0.6213
Therefore, the probability that a renter selected at random is 45 years of age or older is 0.6213.
To answer these questions, we need to use the information provided about the age distribution of renters in the city. Let's calculate the probabilities step by step.
(a) To find the probability that an adult selected at random from this population is a renter, we need to consider the percentage of renters in each age group and their respective proportions in the adult population.
First, let's find the proportion of renters in each age group. We'll multiply the percentage of renters by the percentage of the adult population in each age group.
Proportion of renters in the 21-44 age group = (64% / 100%) * (53% / 100%) = 0.3392
Proportion of renters in the 45-64 age group = (43% / 100%) * (29% / 100%) = 0.1247
Proportion of renters in the 65 and over age group = (62% / 100%) * (18% / 100%) = 0.1116
Next, we add up these proportions to get the overall probability of selecting a renter:
Probability of selecting a renter = 0.3392 + 0.1247 + 0.1116 ≈ 0.5755
Therefore, the probability that an adult selected at random from this population is a renter is approximately 0.5755 or 57.55%.
(b) To find the probability that a renter selected at random is in the 21-44 age bracket, we need to calculate the proportion of renters in the 21-44 age group compared to the total proportion of renters.
Proportion of renters in the 21-44 age group = (64% / 100%) * (53% / 100%) = 0.3392
To find the probability, we divide this proportion by the overall probability of selecting a renter calculated in part (a):
Probability of selecting a renter from the 21-44 age group = 0.3392 / 0.5755 ≈ 0.5889
Therefore, the probability that a renter selected at random is in the 21-44 age bracket is approximately 0.5889 or 58.89%.
(c) To find the probability that a renter selected at random is 45 years of age or older, we need to calculate the proportion of renters who are 45 years of age or older compared to the total proportion of renters.
Proportion of renters who are 45 years of age or older = (43% / 100%) * (29% / 100%) + (62% / 100%) * (18% / 100%) = 0.1247 + 0.1116 ≈ 0.2363
To find the probability, we divide this proportion by the overall probability of selecting a renter calculated in part (a):
Probability of selecting a renter who is 45 years of age or older = 0.2363 / 0.5755 ≈ 0.4107
Therefore, the probability that a renter selected at random is 45 years of age or older is approximately 0.4107 or 41.07%.