To find the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11, we follow these steps:
1. Identify the total number of people who are older than 35 years:
According to the table, the numbers of people older than 35 years in each hemoglobin level category are:
- Less than 9: 76
- Between 9 and 11: 40
- Above 11: 162
Adding these values gives the total number of people older than 35 years:
[tex]\[
76 + 40 + 162 = 278
\][/tex]
2. Identify the number of people older than 35 years with a hemoglobin level between 9 and 11:
The number of people older than 35 years with a hemoglobin level between 9 and 11 is given as 40.
3. Calculate the probability:
The probability is found by dividing the number of people older than 35 years with a hemoglobin level between 9 and 11 by the total number of people older than 35 years:
[tex]\[
\text{Probability} = \frac{\text{Number of people with hemoglobin level between 9 and 11}}{\text{Total number of people older than 35 years}}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Probability} = \frac{40}{278} \approx 0.1439
\][/tex]
Thus, the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is approximately [tex]\(0.1439\)[/tex].
Since [tex]\(0.1439\)[/tex] is not one of the provided answer choices (A, B, C, or D), there might be a mistake in the question's options or the table data provided. Otherwise, based on the given table data, the correct probability calculation is as described above.
