To determine the correct sentence describing the data set, we need to focus on the range where 68% of the data points lie in a normal distribution with the given mean (147) and standard deviation (4).
For a normal distribution:
- 68% of the data points lie within one standard deviation of the mean.
Given:
- Mean (μ) = 147
- Standard deviation (σ) = 4
Therefore, we calculate the bounds as follows:
- Lower bound = Mean - Standard deviation = 147 - 4 = 143
- Upper bound = Mean + Standard deviation = 147 + 4 = 151
Hence, 68% of the data points lie between 143 and 151.
Now, we compare this range with the given options:
O A.
68% of the data points lie between 10 and 14. (Incorrect)
O B.
68% of the data points lie between 8 and 12. (Incorrect)
О с.
68% of the data points lie between 10 and 16. (Incorrect)
O D.
68% of the data points lie between 10 and 18. (Incorrect)
None of the given options describe the correct range for 68% of the data points. The correct description should be:
68% of the data points lie between 143 and 151.
