Question

This is bird migration time. an ornithologist measures the weight of samples of canada geese. he takes 81 samples with a mean of 1.5 kg and a standard deviation of 0.75 kg. what weight would put a sample in the top 5% by weight?

Answer 1

To determine the top 5% weight for the Canada geese, we calculate the corresponding weight using the mean, standard deviation, and z-score for the top 5%, which is approximately 2.73375 kg.

Step-by-step explanation:

To find the weight that would put a sample of Canada geese in the top 5% by weight, we need to use the concept of standard deviation and the normal distribution. Since we have the mean weight of the geese (1.5 kg) and the standard deviation (0.75 kg), we can use these values to calculate the z-score that corresponds to the top 5%. The z-score tells us how many standard deviations away from the mean an observation needs to be to fall into a certain percentile.

Looking at a z-table or using a statistical calculator, we find that the z-score for the top 5% is approximately 1.645. To convert this z-score into a weight, we use the formula:

Weight = mean + (z-score × standard deviation)

Replacing with the known values, we get:

Weight = 1.5 kg + (1.645 × 0.75 kg)

Calculating this results in:

Weight = 1.5 kg + 1.23375 kg

Weight = 2.73375 kg

Therefore, a sample of Canada geese that weighs approximately 2.73375 kg would be in the top 5% by weight.