Question

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

Answer 1

Answer:

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