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?

... Please see the attached file. The Central Limit Theorem is investigated using the rolling dice experiment. The solution is detailed and has a '5/5' rating. ...

... 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...