Answer:
0.3569 is the probability that they have a mean pregnancy between 266 days and 268 days.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 268 days
Standard Deviation, σ = 15 days
We are given that the distribution of lengths of pregnancies is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling =
[tex]\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{64}} = \frac{15}{8}[/tex]
P(pregnancy between 266 days and 268 days)
[tex]P(266 \leq x \leq 268) = P(\displaystyle\frac{266 - 268}{\frac{15}{8}} \leq z \leq \displaystyle\frac{268-268}{\frac{15}{8}}) = P(-1.0667 \leq z \leq 0)\\\\= P(z \leq 0) - P(z < -1.067)\\= 0.5000 - 0.1431 = 0.3569 = 35.69\%[/tex]
[tex]P(266 \leq x \leq 268) = 35.69\%[/tex]
