Problem
Scarlett rolled a die 100 times and 13 of the 100 rolls came up as a six. She wanted to see how likely a result of 13 sixes in 100 rolls would be with a fair die, so Scarlett used a computer simulation to see the proportion of sixes in 100 rolls, repeated 100 times. Create an interval containing the middle $95 \%$ of the data based on the data from the simulation, to the nearest hundredth, and state whether the observed proportion is within the margin of error of the simulation results. (Note: don't use percents for the interval or sample proportion.)
Solution
Step 1 ：Calculate observed proportion: 0.13
Step 2 ：Calculate expected proportion: 0.1667
Step 3 ：Calculate standard deviation: 0.0373
Step 4 ：Calculate margin of error: 0.0731
Step 5 ：Calculate interval: (0.0936, 0.2398)
Step 6 ：Check if observed proportion is within margin of error: Yes
