SOLUTION: The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. Use t
Algebra.Com
Question 1168870: The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. Use the 68-95-99.7 Rule to answer the following questions.
(a) What percentage of pregnancies last between 250 and 282 days?
(b) What percentage of pregnancies last fewer than 250 days?
(c) What percentage of pregnancies last between 266 and 298 days?
(d) What percentage of pregnancies last more than 298 days?
(e) What percentage of pregnancies last between 234 and 282 days?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
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.
RELATED QUESTIONS
The length of human pregnancies from conception to birth varies according to a... (answered by edjones)
The length of human pregnancies from conception to birth varies according to a... (answered by stanbon)
The length of human pregnancies from conception to birth varies according to a... (answered by ewatrrr)
The length of elephant pregnancies from conception to birth varies according to a... (answered by ewatrrr)
(i).The length of human pregnancies from conception to birth approximates a normal... (answered by ewatrrr,stanbon)
The length of human pregnancies varies normally with a mean of 266 days and a standard... (answered by amfagge92)
Hi... I'm stuck, and don't know where to begin.
The length of human pregnancies varies (answered by Fombitz)
The length of human pregnancies varies normally with a mean of 266 days and a standard... (answered by Fombitz)
The length of human pregnancies varies normally with a mean of 266 days and a standard... (answered by amfagge92)