Final answer:
To find the probability of a pregnancy lasting less than 265 days in a normal distribution with a mean of 280 days and standard deviation of 13 days, we calculate the z-score and look up the corresponding probability in the standard normal distribution table. The exact probability isn't provided without the table values, but the method is outlined.
Step-by-step explanation:
To find the probability that a randomly selected pregnancy lasts less than 265 days, given the normal distribution of human pregnancies, we need to use the provided information about the mean and standard deviation. If we consider the mean (μ) to be 280 days and the standard deviation (σ) to be 13 days, the z-score can be calculated using the formula: z = (X - μ) / σ, where X is the value we are comparing to the mean.
For a pregnancy lasting less than 265 days, we calculate: z = (265 - 280) / 13 = -15 / 13 ≈ -1.15. Once we have the z-score, we can use the standard normal distribution table to give us the area to the left of this z-score which corresponds to the sought probability.
Therefore, looking up the value for z = -1.15 in the standard normal distribution table, we would find a corresponding probability value. However, since the question does not provide the exact values from the table, we cannot give the exact probability. Nevertheless, the probability would generally be close to the table value for z = -1.15.