I am working on a problem with a normal probability distribution but I am unsure of the results I calculated the probability asked for but still hesitate regarding the output and especially the first question
the following is the image upload : http://tinypic.com/r/lyueh/8 and the total number of people is respectively :
Age group (years)
0–14 15–24 25–34 35–44 45–54 55–64 65–74 "75 years and over" Males Females Persons
4,209.3 3,043.2 3,206.3 3,137.6 3,023.0 2,565.6 1,680.7 1,239.5 11,003.5 11,101.7 22,105.3
a) What is the probability that a person, randomly selected, has mood (affected) problems and belongs to the age group 35 to 44?
P(A and B) = P(A) * P(B|A)
A= event of a person having mood problem
B= belonging to the age of 35-44
P(A)=total persons * total persons with mood problems = 2143 / 22105 = 0.096
P(B|A) = people belonging to age 35-44 with mood problem / total number of people with mood =
402 / 2143 = 0.187
P(A and B) = 0.096 * 0.187 = 0.0179
b)What is the probability that a person, randomly selected, belongs to the age group of 55 or over?
Number of people at 55-64 + 65-74 + 75 years and over = 2566+1681+1240= 5487
P(A) = number of people at age 55 and over / total number of people = 5487 / 22105 = 0.248
c)Given that the person belongs to the age group of 45 to 54, what is the probability that he or she is suffering from alcohol and drug problems?
Total number of people at age 45-54 = 3023
Number of people suffering from drug and alcohol problems at 45-54 = 35.9
P(A) = 35.9/3023 = 0.0118
d)Are different types of mental and behavioral problems independent of the gender?
Thank you Much appreciated!