## To answer the questions about the insects captured in a trap, we need to use the properties of a normal distribution.

a) To find the probability of capturing between 2500 and 3500 insects, we need to calculate the z-scores for these values and then use a z-table or a statistical calculator.

The z-score formula is: z = (x - Î¼) / Ïƒ

where x is the value, Î¼ is the mean, and Ïƒ is the standard deviation.

For 2500 insects: z = (2500 - 2950) / 550 = -0.818

For 3500 insects: z = (3500 - 2950) / 550 = 1

Using a z-table or a statistical calculator, we can find the area (probability) between these two z-scores. The probability of capturing between 2500 and 3500 insects is the difference between these two probabilities.

b) To find the maximum number of insects that would trigger a trap relocation on a given night (lowest 5%), we need to find the z-score corresponding to the lowest 5% of the distribution.

Using a z-table or a statistical calculator, we can find the z-score that corresponds to the cumulative probability of 5%. Once we have the z-score, we can use the formula to find the maximum number of insects:

Max insects = (z * Ïƒ) + Î¼

c) To find the probability of capturing between 2600 and 2850 insects, we follow the same steps as in part a. Calculate the z-scores for these values and find the area between the z-scores using a z-table or a statistical calculator.

d) To find the minimum number of insects that would trigger calling an exterminator on a given night (highest 10%), we need to find the z-score corresponding to the highest 10% of the distribution.

Using a z-table or a statistical calculator, we can find the z-score that corresponds to the cumulative probability of 90%. Once we have the z-score, we can use the formula to find the minimum number of insects:

Min insects = (z * Ïƒ) + Î¼

Regarding the statistic that best describes the size of a chicken egg, the mean (Î¼) would be the most appropriate statistic. The mean represents the average size of the eggs in the given set of six sizes (15, 18, 21, 24, 27 and 30 ounces per dozen). It provides a measure of central tendency, giving us a representative value for the size of chicken eggs.