Chapter 5.1, Problem 21E

(a)

To determine

To explain how would you use random digits to imitate one repetition of the process and find out what variable would you measure.

Answer to Problem 21E

The number of repeated numbers is measured.

Explanation of Solution

To use random digits to imitate one repetition of the process, can be done as:

Use three digit numbers.

If the numbers is between $000\text{ and 364}$ , then it corresponds with a birthday.

If the number is between $\text{364 and 999}$ , then the number should be ignored.

Draw $\text{30}$ numbers between $000\text{ and 364}$ randomly.

Then count the number of repeated numbers in the list of $\text{30}$ numbers.

The number of repeated numbers is measured.

(b)

To determine

To use the technology to perform five repetition and record it.

Explanation of Solution

Use three digit numbers.

If the numbers is between $000\text{ and 364}$ , then it corresponds with a birthday.

If the number is between $\text{364 and 999}$ , then the number should be ignored.

Draw $\text{30}$ numbers between $000\text{ and 364}$ randomly.

Then count the number of repeated numbers in the list of $\text{30}$ numbers.

Using your $Ti83/Ti84$ -calculator, you can use the following command for one simulation:

  $randInt\left(0,364,30\right)$

where the command randInt can be found in the MATH-menu under PRB.

Repeat the simulation five times.

Determine the number of repetitions in each simulation.

(c)

To determine

To explain would you be surprised or not to learn that theoretical probability is $0.71$ and explain why or why not.

Answer to Problem 21E

It is not surprising.

Explanation of Solution

The theoretical probability of $0.71$ is not surprising, because in exercise (b) we noted that (nearly) all simulations had repeated birthdays. Thus it is not surprising.