In the next activity, you will roll a standard number cube 35 times.

1. Draw a dot plot that shows the distribution of values you might expect for the rolls. Explain your reasoning.

   

2. If you rolled the number cube 1 million times and found the mean of all the values, what would you expect for the mean? Explain your reasoning.

Roll your number cube 35 times, and record the values as you roll.

1. Every 5 values, find the mean.

   rolls	1–5	6-10	11-15	16-20	21-25	26-30	31-35
   mean

2. Share your means with your group, and create a dot plot of all the means from your group.

   

3. What do you notice about the shape of the distribution of means?
4. Using the dot plot of means, what do you think is a good estimate for the mean of all 140 rolls from your group? How does this value compare to your estimate from the Warm-up?

As with the means of sample proportions, when there is a large sample size or when the population distribution is approximately normal, the means of sample means are usually within 2 standard deviations of the sampling distribution of the means of the population mean. For each situation, use the sample data to estimate the mean for the population, and use the standard deviation from the sampling distribution to give a margin of error.

1. In 2010, a sample of 10 gas stations was selected at random, and the price of regular gasoline was recorded for each gas station. After many simulations, the sampling distribution has a standard deviation of $0.13.
   • 2.38
   • 2.42
   • 2.64
   • 2.35
   • 2.65
   • 2.47
   • 2.67
   • 2.59
   • 2.63
   • 2.41
2. A sample of claimed UFO sightings in 13 randomly selected locations was recorded. After many simulations, the sampling distribution has a standard deviation of 158.1 sightings.
   • 400
   • 427
   • 892
   • 640
   • 713
   • 614
   • 725
   • 477
   • 460
   • 445
   • 476
   • 336
   • 536
3. A company producing baseballs selects 9 baseballs at random and measures the diameter in centimeters. After many simulations, the sampling distribution has a standard deviation of 0.22 centimeters.
   • 7.5
   • 7.6
   • 7.2
   • 7.4
   • 7.2
   • 7.3
   • 7.5
   • 6.9
   • 7.5
4. A publisher takes a random sample of 15 people to determine the number of minutes they spend reading a newspaper. After many simulations, the sampling distribution has a standard deviation of 1.5 minutes.
   • 11.1
   • 9.2
   • 8.1
   • 10.5
   • 10
   • 9.7
   • 7.7
   • 11.8
   • 11.1
   • 7.6
   • 6.3
   • 9.4
   • 10.4
   • 8.7
   • 10.2