Question 1168870
Let's use the 68-95-99.7 Rule to answer these questions.

**Understanding the 68-95-99.7 Rule**

* In a normal distribution:
    * Approximately 68% of the data falls within 1 standard deviation of the mean.
    * Approximately 95% of the data falls within 2 standard deviations of the mean.
    * Approximately 99.7% of the data falls within 3 standard deviations of the mean.

**Given Information**

* Mean (µ) = 266 days
* Standard deviation (σ) = 16 days

**Calculations**

* µ - σ = 266 - 16 = 250
* µ + σ = 266 + 16 = 282
* µ - 2σ = 266 - 32 = 234
* µ + 2σ = 266 + 32 = 298
* µ - 3σ = 266 - 48 = 218
* µ + 3σ = 266 + 48 = 314

**(a) What percentage of pregnancies last between 250 and 282 days?**

* This is the range of µ - σ to µ + σ, which is 1 standard deviation from the mean.
* Therefore, approximately 68% of pregnancies last between 250 and 282 days.

**(b) What percentage of pregnancies last fewer than 250 days?**

* 250 days is µ - σ.
* Since 68% of pregnancies fall within 1 standard deviation of the mean, 32% fall outside of it (100% - 68% = 32%).
* Because the normal distribution is symmetrical, half of the 32% falls below 250 days.
* 32%/2 = 16%
* Therefore, approximately 16% of pregnancies last fewer than 250 days.

**(c) What percentage of pregnancies last between 266 and 298 days?**

* 266 is the mean (µ).
* 298 is µ + 2σ.
* 95% of the data falls within 2 standard deviations. That means 47.5% of the data falls between the mean, and two standard deviations above the mean.
* Therefore, approximately 47.5% of pregnancies last between 266 and 298 days.

**(d) What percentage of pregnancies last more than 298 days?**

* 298 is µ + 2σ.
* 95% of the data falls within 2 standard deviations. That leaves 5% outside of that range.
* Because the normal distribution is symmetrical, half of the 5% falls above 298 days.
* 5%/2 = 2.5%
* Therefore, approximately 2.5% of pregnancies last more than 298 days.

**(e) What percentage of pregnancies last between 234 and 282 days?**

* 234 is µ - 2σ.
* 282 is µ + σ.
* The range between 234 and 266 is 47.5% of the data.
* The range between 266 and 282 is 34% of the data.
* 47.5% + 34% = 81.5%
* Therefore, approximately 81.5% of pregnancies last between 234 and 282 days.