A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?

To determine the interval that would contain approximately 95% of the measurements for a large population with a bell-shaped (normal) distribution, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, in a normal distribution, approximately 95% of the data will lie within two standard deviations of the mean.

In this case, the mean is 200, and the standard deviation is 40. Therefore, to find the interval that encompasses 95% of the measurements, you subtract and add two times the standard deviation from the mean:

1. Calculate two standard deviations:

2 × 40 = 80

2. Determine the lower and upper bounds of the interval:

• Lower bound: 200 - 80 = 120

• Upper bound: 200 + 80 = 280

Thus, the interval that contains approximately 95% of the measurements is from 120 to 280. This aligns with option C, which is the correct choice.

The other options do not capture the correct interval of 120 to 280, thereby including too narrow or too wide ranges that do not correspond to the 95% threshold defined by the empirical