MathStat474 - HW 9

Posted on Tue Mar 12. Due: WED March 27.

Problem 1.

Length (in days) of a randomly chosen human pregnancy is a normal random varialbe with \(\mu=266\) and \(\sigma=16\).

Find Q1, the median, and Q3.
What is the probability that a randomly chosen pregnancy will last less than 246 days?
What is the probability that a randomly chosen pregnancy will last longer than 240 days?
What is the probability that a randomly chosen pregnancy will last longer than 500 days?
Suppose a pregnant person’s spose has scheduled their business trip so that they will be in town between 235th and 295th days. What is the probability that the birth will take place during that time?

Make sure you use standardized values to solve this problem. You can also solve integrals, for which you MUST show your work; or you can use software, in which case you MUST print out the code you used. Otherwise, look up the Z-tables and indicate how you arrived at the answers.

The standard normal Z-table is posted on the site (copy from the back of our textbook). If you are using it please highlight the cell in the table where you looked up the desired value!

Problem 2.

Solve exercise 6.1..

Problem 3.

Solve exercise 6.3..

Problem 4.

Solve exercise 6.11..

Problem 5.

Solve exercise 6.33..

Problem 6.

Solve exercise 4.12.. In this problem we are practicing to compute the mean of a random variable.

Problem 7.

Solve exercise 4.37.. In this problem we are practicing to compute the variance of a random variable.

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