In Canada, it is estimated that in the population of ages 15 to 64, 16% of women
ID: 3238204 • Letter: I
Question
In Canada, it is estimated that in the population of ages 15 to 64, 16% of women and 8% of men suffer from depression. According to the census data released by Statistics Canada in October 2009, the ratio between the male and female populations for the Canadian adults aged 15 to 64 is 0.83.
a) What percentage of the Canadian population aged 15 to 64 consists of females?
b) What is the probability that a randomly chosen person of age 15 to 64 suffers from depression?
c) Is depression independent of gender?
d) What is the probability that a randomly chosen person is a female, given that the person suffers from depression?
Explanation / Answer
Solution:-
In Canada, it is estimated that in the population of ages 15 to 64, 16% of women and 8% of men suffer from depression. According to the census data released by Statistics Canada in October 2009, the ratio between the male and female populations for the Canadian adults aged 15 to 64 is 0.83.
a) What percentage of the Canadian population aged 15 to 64 consists of females?
let, M = Male and F = Female
given,
M : F = 0.83 = 83 : 100
%F = 100 / (83 + 100) (100%) = 54.64%
b) What is the probability that a randomly chosen person of age 15 to 64 suffers from depression?
let P(D) = randomly selected person suffers from depression
P(D) = [ 8%(83) + 16%(100) ] /(83 + 183)
P(D) = (6.64 + 16)/(183)
P(D) = 22.64/183 = 0.1237
c) Is depression independent of gender?
An independent variable is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable. Other factors (such as what they eat, how much they go to school, how much television they watch) aren't going to change a person's age. In fact, when you are looking for some kind of relationship between variables you are trying to see if the independent variable causes some kind of change in the other variables, or dependent variables.
So, depression is independent of gender.
d) What is the probability that a randomly chosen person is a female, given that the person suffers from depression?
P(F I D) = P(F and D) / P(F)
= (0.5464 * 0.1237) / 0.5464 = 0.1237