A recent social survey asked whether respondents believed that Antarctic penguins were threatened. The responses are summarized in the table below.
Answer Male Female Total
A great deal 123 200 323
Some 150 164 314
Not at all 28 16 44
Total 301 380 681
A respondent is randomly selected among those who believe that penguins are threatened "a great deal." Approximately what is the probability that this respondent will be female?
a
29%
b
62%
c
53%
d
38%
The probability would be:
[Number of Females who answered "A great deal"] / [Total number of respondents who answered "A great deal"]
= 200 / 323
≈ 0.62
So the answer is (b) 62%.
are you sure
Yes, I am sure. We are asked to find the probability that a randomly selected respondent who believes that penguins are threatened "a great deal" is a female. This means we need to consider only the total number of respondents who answered "A great deal," which is 323.
Out of these 323 respondents, 200 are females.
Therefore, the probability of selecting a female respondent who answered "A great deal" is:
200/323 = 0.6198 ≈ 0.62 (rounded to two decimal places)
So, the option (b) 62% is the correct answer.
To find the probability that a randomly selected respondent who believes penguins are threatened "a great deal" is female, we need to divide the number of females who answered "a great deal" by the total number of respondents who answered "a great deal."
From the table, we can see that the number of females who answered "a great deal" is 200. The total number of respondents who answered "a great deal" is 323.
The probability is calculated by dividing the number of females who answered "a great deal" (200) by the total number of respondents who answered "a great deal" (323):
Probability = Number of females who answered "a great deal" / Total number of respondents who answered "a great deal"
Probability = 200 / 323
To approximate this percentage, divide 200 by 323 and multiply by 100:
Probability ≈ (200 / 323) × 100
Probability ≈ 0.619 × 100
Probability ≈ 61.9%
Therefore, the approximate probability that a randomly selected respondent who believes penguins are threatened "a great deal" is female is 61.9%. The closest option in the given choices is 62% (option b).