Respuesta :
Answer:
The range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].
Step-by-step explanation:
We are given that the lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 17 days.
Let X = lengths of pregnancies in a small rural village
SO, X ~ Normal([tex]\mu=262,\sigma^{2} = 17^{2}[/tex])
Here, [tex]\mu[/tex] = population mean = 262 days
[tex]\sigma[/tex] = standard deviation = 17 days
Now, the 68-95-99.7 rule states that;
- 68% of the data values lies within one standard deviation points.
- 95% of the data values lies within two standard deviation points.
- 99.7% of the data values lies within three standard deviation points.
So, middle 68% of most pregnancies is represented through the range of within one standard deviation points, that is;
[ [tex]\mu -\sigma[/tex] , [tex]\mu + \sigma[/tex] ] = [262 - 17 , 262 + 17]
= [245 days , 279 days]
Hence, the range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].
