The length of human pregnancies from conception to birth is normally distributed with mean 266 days and standard deviation 16 days. What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?

68 %

Step-by-step explanation:

(a) Using the 68-95-99.7% rule, between what two lengths do the most typical 68% of all pregnancies fall?

95%? 99.7%?

The middle 68% of all pregnancies last between 266-16 and 266+16 days, 250 to 282. The middle 95% of all

pregnancies last between 266-2*16 and 266+2*16 days, 234 to 298 (for future reference, note that this “rule” is  

rounded somewhat compared to the charts). The middle 99.7% of all pregnancies last between 266-3*16 and

266+3*16 days, 218 to 314.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

7/2

(decimal: 3.5)

welcome ; )

step-by-step explanation: