what is the probability that a random sample of 25 pregnancies has a mean gestation period of 258 days or less? standard deviation of 16 days.

Answer 1

To solve this problem, we can use the central limit theorem, which states that the distribution of sample means approximates a normal distribution as the sample size increases.

Given:
Sample size (n) = 25
Mean (μ) = 258 days
Standard deviation (σ) = 16 days

First, calculate the standard error (SE) using the formula:
SE = σ / √n
SE = 16 / √25
SE = 16 / 5
SE = 3.2

Next, calculate the z-score using the formula:
z = (x - μ) / SE
where x is the value we are interested in (258 days).

z = (258 - 258) / 3.2
z = 0

Since the z-score is 0, the probability is equivalent to the area under the curve to the left of 0 in the standard normal distribution. Using a z-table or a statistical software, this probability is found to be approximately 0.5000.

Therefore, the probability that a random sample of 25 pregnancies has a mean gestation period of 258 days or less is 0.5000 or 50%.