Answer:
The probability that 200 women have a mean pregnancy between 266 days and 268 days is 0.371.
Explanation:
Let X = gestation time for humans.
The mean of the random variable X is: E (X) = μ = 266 days.
The standard deviation of the random variable X is: SD (X) = σ = 25 days.
**Assume that the gestation time for humans follows a Normal distribution.
The z-score for the sample mean is: [tex]z=\frac{\bar x-\mu}{\sigma/ \sqrt{n}}[/tex].
The sample of women selected is: n = 200.
Compute the probability that 200 women have a mean pregnancy between 266 days and 268 days as follows:
[tex]P(266\leq \bar X\leq \leq 268)=P(\frac{266-266}{25/ \sqrt{200}}\leq \frac{\bar X-\mu}{\sigma/ \sqrt{n}}\leq \frac{268-266}{25/ \sqrt{200}})\\=P(0\leq Z\leq 1.13)\\=P(Z<1.13)-P(Z<0)\\=0.871-0.50\\=0.371[/tex]
**Use the z-table for the probability.
Thus, the probability that 200 women have a mean pregnancy between 266 days and 268 days is 0.371.
