To solve this problem, we can use the standard normal distribution and the Z-score formula to find the probability that a pregnancy will last at least 300 days.
The Z-score is a measure of how many standard deviations a value is from the mean. We can use the Z-score to standardize a value, which means we can express it in terms of how many standard deviations it is from the mean of the distribution.
The Z-score formula is:
Z = (x - μ) / σ
Where x is the value we are standardizing, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
To find the probability that a pregnancy will last at least 300 days, we can use the Z-score formula to standardize 300 days:
Z = (300 - 268) / 15 = 4
This means that 300 days is 4 standard deviations above the mean of 268 days.
To find the probability that a pregnancy will last at least 300 days, we can use a Z-table or a calculator to find the area under the standard normal curve that is greater than or equal to 4 standard deviations.
Using a calculator or a Z-table, we find that the probability that a pregnancy will last at least 300 days is approximately 0.0165, which corresponds to answer choice D: 0.0165.