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Tems11 [23]
2 years ago
14

The gestation time for humans has a mean of 266 days and a standard deviation of 25 days. If 200 women are randomly selected, fi

nd the probability that they have a mean pregnancy between 266 days and 268 days.

Biology
1 answer:
Yuki888 [10]2 years ago
8 0

Answer:

The probability that 200 women have a mean pregnancy between 266 days and 268 days is 0.371.

Explanation:

Let <em>X</em> = gestation time for humans.

The mean of the random variable <em>X</em> is: E (X) = <em>μ</em> = 266 days.

The standard deviation of the random variable <em>X</em> is: SD (X) = <em>σ</em> = 25 days.

**Assume that the gestation time for humans follows a Normal distribution.

The <em>z</em>-score for the sample mean is: z=\frac{\bar x-\mu}{\sigma/ \sqrt{n}}.

The sample of women selected is:<em> </em><em>n</em> = 200.

Compute the probability that 200 women have a mean pregnancy between 266 days and 268 days as follows:

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

**Use the <em>z</em>-table for the probability.

Thus, the probability that 200 women have a mean pregnancy between 266 days and 268 days is 0.371.

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