g The lengths of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. A study enrolls a random sample of 25 pregnant women. Assuming all appropriate conditions are met, what is the probability that the average pregnancy length of the women in the study is more than 268 days

0.26599

Step-by-step explanation:

When given a random number of samples, we solve using this z score formula

z = (x-μ)/σ/√n

where x is the raw score = 268

μ is the population mean = 266

σ is the population standard deviation = 16

n = 25

For x > 268

z = 268 - 266/16/√25

z= 2/16/5

z =0.625

Probability value from Z-Table:

P(x<268) = 0.73401

P(x>268) = 1 - P(x<268)

P(x>268) = 1 - 0.73401

P(x>268) = 0.26599

The probability that the average pregnancy length of the women in the study is more than 268 days is 0.26599

, 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

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x