Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The lengths of pregnancies are normally distributed with a mean of 268 days and

ID: 3049218 • Letter: T

Question

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 307 days or longer. b. If the length of pregnancy is in the lowest 2%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

a. The probability that a pregnancy will last307days or longer is

(Round to four decimal places as needed.)

b. Babies who are born on or before ______days are considered premature.

(Round to four decimal places as needed.)

Explanation / Answer

Mean = 268 days

Standard deviation = 15 days

P(X < A) = P(Z < (A - mean) / standard deviation)

A) P(a pregnancy will last 307 days) = P(X > 307)

= 1 - P(X < 307)

= 1 - P(Z < (307 - 268)/15)

= 1 - P(Z < 2.6)

= 1 - 0.9953

= 0.0047

B) Let the babies born befor P days be considered premature

P(X < P) = 0.02

P(Z < (P - 268)/15) = 0.02

From standard normal distribution table,

(P - 268)/15 = -2.05

P = 237.28 days

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote