What is the mean number of rolls of a die before a 1 is observed? Roll a die until a 1 is observed. Repeat this process 30 times and answer the following questions.

1. Obtain a point estimate of the mean number of rolls of a die before a 1 is observed.

2. The population standard deviation for the number of rolls before a 1 is observed. Use this result to construct a 90% Z-interval for the mean number of rolls required before a 1 is observed.

3. The population mean number of rolls before a 1 is observed is 6. Does your interval include 6? What proportion of the Z-intervals in the class included 6? How many did you expect to include 6?

4. Construct a 90% t-interval for the mean number of rolls required before a 1 is observed.

5. The population mean number of rolls before a 1 is observed is 6. Does your interval include 6?

6. What proportion of the t-intervals in the class includes 6? How many did you expect to include 6?

7. Compare the Z-interval with the t-interval. Which has the smaller margin of error?

Solution Summary

An experiment of rolling a dice a number of times to test a particular number (say 1) to appear on top.

... Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added ... the outcome of a single trial of a random experiment. ...

... total number of times we did the experiment we calculate a reasonable, empirically based, estimate of the probability that rolling this six-sided die one time ...

... the theoretical probability of rolling "snake eyes" or two ones with a pair of dice. Compare the theoretical probability of the results of Mike's experiment. ...

... b. Roll a pair of fair dice 24 times, record the pair on top. For experiment a, find the probability of event A: at least one 6. For the second experiment...

... p). figure out how many times you are running the experiment (n), and ... Like in the dice example ... How many ways can you roll a die 4 k 4 times ...