Question

answer the question based on the data in the table.
13
select the correct answer.
what is the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11?
a. 0.257
b. 0.284
c. 0.312
d. 0.356
e. 0.548

hemoglobin level	less than 25 years	25 - 35 years	above 35 years	total
between 9 and 11	49	52
above 11	69		40
total	139	128	162	429

Explanation:

Step1: Find missing value (Above 35, 9-11)

First, calculate the total number of people with hemoglobin between 9 and 11:
Total for "Between 9 and 11" = Overall total - (Total <9 + Total >11)
First find Total >11: $139 + 128 + 162 - 129 - (49+52+?)$ is simpler to use row totals:
Total for "Above 11" = Total of "Less than 25" (Above11) + "25-35" (Above11) + "Above35" (Above11)
We know total of "25-35" column is 128, so "25-35" (Above11) = $128 - 32 - 52 = 44$
Total "Above 11" = $69 + 44 + 40 = 153$
Total "Between 9 and 11" = $429 - 129 - 153 = 147$
Now find "Above 35, Between 9 and 11" = $147 - 49 - 52 = 46$

Step2: Calculate conditional probability

We need probability that hemoglobin is 9-11 given age >35.
Formula: $P(\text{9-11} | \text{>35}) = \frac{\text{Number of >35 with 9-11}}{\text{Total >35}}$
$\text{Number of >35 with 9-11} = 46$, $\text{Total >35} = 162$
Expression: $\frac{46}{162} \approx 0.284$

Answer:

B. 0.284