Final answer:
The birth weight of domestic cats at the 20th percentile, assuming a normal distribution with a mean of 3 ounces and a standard deviation of 0.4 ounce, is approximately 2.66 ounces.
Step-by-step explanation:
Given the average birth weight of domestic cats is about 3 ounces with a standard deviation of 0.4 ounce, and assuming a normal distribution, we need to find the birth weight that corresponds to the 20th percentile. The value corresponding to the 20th percentile (P20) can be found using the z-score for the 20th percentile and the formula:
P20 = μ + (z * σ)
where μ is the mean and σ is the standard deviation. A z-score represents the number of standard deviations a data point is from the mean. The z-score for the 20th percentile is approximately -0.84. Using the provided mean (3 ounces) and standard deviation (0.4 ounce), we can calculate:
P20 = 3 + (-0.84 * 0.4) = 3 - 0.336 = 2.664 ounces
The closest answer among the options is (b) 2.66 ounces, which is the weight of cats at the 20th percentile.