# What is the mean number of rolls of a die before a 1 is observed

What is the mean number of rolls of a die before a 1 is observed ? Either as an individual or in a small group, roll a die until a 1 is observed. Repeat this process 30 times.

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

(b) The population standard deviation for the number of rolls before a 1 is observed is square root of 30. Use this result to construct a 90 % Z-interval for the mean number of rolls required before a 1 is observed.

(c) 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 includes 6? How many did you expect to include 6 ?

(d) Construct a 90% T-interval for the mean number of rolls required before a 1 is observed.

(e) The population mean number of rolls before a 1 is observed is 6. Does your interval include 6? What proportion of the t-intervals in the class includes 6? How many did you expect to include 6?

(f) Compare the Z-interval with the t-interval. Which has the smaller margin of error? Why?

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