The length of human pregnancies is approximately normal with mean u = 266 days and standard deviation a = 16 days. If 100 indonendent random samoles of size n = 23 pregnancies were obtained from this population, we would expect ? to have a sample mean of 260 days or less

Step 1 ：The length of human pregnancies is approximately normal with mean \(\mu = 266\) days and standard deviation \(\sigma = 16\) days.

Step 2 ：If 100 independent random samples of size \(n = 23\) pregnancies were obtained from this population, we want to find out how many would have a sample mean of 260 days or less.

Step 3 ：The sampling distribution of the mean is normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Step 4 ：We calculate the z-score for a sample mean of 260 days, which tells us how many standard deviations below the mean this value is.

Step 5 ：We use the standard normal distribution to find the probability that a sample mean is less than or equal to 260 days.

Step 6 ：We multiply this probability by the number of samples to find the expected number of samples with a mean of 260 days or less.

Step 7 ：The expected number of samples with a mean of 260 days or less is approximately 3.6. However, since we can't have a fraction of a sample, we should round this number to the nearest whole number.

Step 8 ：Final Answer: The expected number of samples with a mean of 260 days or less is approximately \(\boxed{4}\).