Answer :
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.
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.
