Question

the partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a retirement home.

	60-69	70-79	over 79	total
female	19	2	4
total

what is the probability that a resident is female ? round your answer to three decimal places if necessary.
a. 0.635 \t\t c. 0.62
b. 0.629 \t\t d. 0.625

please select the best answer from the choices provided

Explanation:

Step1: Calculate total female residents

Sum the number of female residents in each age group: \(19 + 2 + 4 = 25\)

Step2: Calculate total male residents

Sum the number of male residents in each age group: \(1 + 9 + 5 = 15\)

Step3: Calculate total residents

Add total male and total female residents: \(25 + 15 = 40\)

Step4: Calculate probability of female resident

Probability is total female divided by total residents: \(\frac{25}{40} = 0.625\)? Wait, no, wait. Wait, 19+2+4 is 25? Wait 19+2 is 21, 21+4 is 25. Male: 1+9=10, 10+5=15. Total is 25+15=40. Then probability female is 25/40? Wait 25 divided by 40 is 0.625? But let's check again. Wait 19 (female 60-69) + 2 (female 70-79) +4 (female over 79) = 25. Male: 1+9+5=15. Total 40. So 25/40 = 0.625? But wait the options have 0.629? Wait maybe I miscalculated. Wait no, 19+2+4: 19+2 is 21, 21+4 is 25. Male: 1+9=10, 10+5=15. 25+15=40. 25/40=0.625. But option d is 0.625. Wait but let me check again. Wait maybe the total is different? Wait no, the contingency table:

Male: 60-69:1, 70-79:9, Over79:5. So male total:1+9+5=15.

Female:60-69:19, 70-79:2, Over79:4. Female total:19+2+4=25.

Total residents:15+25=40.

Probability female:25/40=0.625. So option d.

Answer:

d. 0.625