If you roll a die 48 times and 8 of the rolls result in a "5," what empirical probability was observed for the event "5"? (Give your answer correct to three decimal places.)
To find the empirical probability of rolling a "5" with a fair die, you need to divide the number of successful outcomes (rolls that result in a "5") by the total number of trials (the number of times the die was rolled). In this case, the number of successful outcomes is 8 (since 8 rolls resulted in a "5") and the total number of trials is 48 (since the die was rolled 48 times).
So, the empirical probability of rolling a "5" can be calculated as follows:
Empirical probability = Number of successful outcomes / Total number of trials
Empirical probability = 8 / 48
Empirical probability = 1 / 6
Empirical probability ≈ 0.167
Therefore, the observed empirical probability for rolling a "5" is approximately 0.167 (rounded to three decimal places).