Answered: a. The probability that a pregnancy…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 309 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 last 309 days or longer is

(Round to four decimal places as needed.)

b. Babies who are born on or before____days are considered premature.

(Round to the nearest integer as needed.)

Expert Solution

Step 1

a. The probability that a pregnancy will last 309 days or longer is

(Round to four decimal places as needed.)

The following information has been provided

$\mu = 268, \text{ } \sigma = 15$

We need to compute $\Pr(X \ge 309)$

The corresponding z-value needed to be computed is:

$Z = \frac{X - \mu}{\sigma} = \frac{ 309 - 268}{ 15} = 2.7333$

Therefore, we get that

$\Pr(X \geq 309) = \Pr\left(Z \ge \frac{ 309 - 268}{ 15}\right) = \Pr(Z \ge 2.7333)$

$= 1 - 0.9969 = 0.0031$

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