Question

In an experimental population of the flour beetle Tribolium castaneum, the pupal weight is distributed normally with a mean of 2.0 mg and a standard deviation of 0.2 mg. What proportion of the population is expected to have a pupal weight between 1.8 and 2.2 mg? Between 1.6 and 2.4 mg?

Answer 1

To find the proportion of the population with a certain pupal weight range, calculate the z-scores for the range and use a z-table or calculator to find the corresponding proportions.

Step-by-step explanation:

To find the proportion of the population with a pupal weight between a certain range, we need to calculate the z-scores for the lower and upper values of the range. The z-score formula is (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For the range 1.8 to 2.2 mg:

Z-score for 1.8 mg = (1.8 - 2.0) / 0.2 = -1

Z-score for 2.2 mg = (2.2 - 2.0) / 0.2 = 1

Using a z-table or calculator, we can find the proportions corresponding to the z-scores. The proportion between -1 and 1 is approximately 0.6827, which is 68.27%.

For the range 1.6 to 2.4 mg:

Z-score for 1.6 mg = (1.6 - 2.0) / 0.2 = -2

Z-score for 2.4 mg = (2.4 - 2.0) / 0.2 = 2

The proportion between -2 and 2 is approximately 0.9545, which is 95.45%.