Question

Suppose babies born after a gestation period of fewer than 37 weeks are considered premature. What percentage of babies born is premature if the gestation period is normally distributed with a mean of 40 weeks and a standard deviation of 2 weeks?

Answer 1

To find the percentage of babies born premature, calculate the z-score for a gestation period of 37 weeks and find the corresponding probability from a standard normal distribution table.

Step-by-step explanation:

To find the percentage of babies born premature, we need to calculate the probability of a baby being born before 37 weeks.

1. First, we need to calculate the z-score using the formula z = (x - μ) / σ, where x is the gestation period, μ is the mean, and σ is the standard deviation.
2. Substituting the given values, we get z = (37 - 40) / 2 = -1.5.
3. Using a standard normal distribution table, we can find the probability corresponding to the z-score. From the table, we find that the probability of a z-score of -1.5 or less is approximately 0.0668.
4. Finally, to find the percentage, we multiply the probability by 100. So, the percentage of babies born premature is approximately 6.68%.