Questions: In which of the following situations is the probability calculated empirically? - A customer satisfaction survey reveals that 270 of the 300 respondents were satisfied with their service, so the estimated customer satisfaction rate is 90%. - A doctor believes that there is a 90% chance his patient will survive a procedure. - A professor has assigned a C grade to 10 of the first 25 exams she graded, so the estimated probability that the next exam will get a C is 40%. - Out of 1000 fans at a rock concert, 600 are male, so if a random person gets called to the stage, the probability that that person will be male is 60%. - A city with 100,000 people has 30,000 Caucasians, so the probability that a random person in this city is Caucasian is 30%.

In which of the following situations is the probability calculated empirically?
- A customer satisfaction survey reveals that 270 of the 300 respondents were satisfied with their service, so the estimated customer satisfaction rate is 90%.
- A doctor believes that there is a 90% chance his patient will survive a procedure.
- A professor has assigned a C grade to 10 of the first 25 exams she graded, so the estimated probability that the next exam will get a C is 40%.
- Out of 1000 fans at a rock concert, 600 are male, so if a random person gets called to the stage, the probability that that person will be male is 60%.
- A city with 100,000 people has 30,000 Caucasians, so the probability that a random person in this city is Caucasian is 30%.

Transcript text: In which of the following situations is the probability calculated empirically? A customer satisfaction survey reveals that 270 of the 300 respondents were satisfied with their service, so the estimated customer satisfaction rate is $90 \%$. A doctor believes that there is a $90 \%$ chance his patient will survive a procedure. A professor has assigned a C grade to 10 of the first 25 exams she graded, so the estimated probability that the next exam will get a C is $40 \%$. Out of 1000 fans at a rock concert, 600 are male, so if a random person gets called to the stage, the probability that that person will be male is $60 \%$. A city with 100,000 people has 30,000 Caucasians, so the probability that a random person in this city is Caucasian is $30 \%$.

Solution

Solution Steps

To determine which situations involve empirical probability, we need to identify cases where the probability is based on actual data or observations rather than theoretical assumptions or personal beliefs. Empirical probability is calculated by dividing the number of favorable outcomes by the total number of observed outcomes.

Step 1: Identify Empirical Probability Situations

Empirical probability is calculated based on actual data or observations. We need to identify situations where the probability is derived from observed data rather than theoretical assumptions or personal beliefs.

Step 2: Analyze Each Situation

Customer Satisfaction Survey: The probability is calculated as $\frac{270}{300} = 0.90$, which is based on actual survey data.
Doctor's Belief: This is a subjective belief and not based on empirical data.
Professor's Exam Grading: The probability is calculated as $\frac{10}{25} = 0.40$, which is based on the grades assigned so far.
Rock Concert Fans: The probability is calculated as $\frac{600}{1000} = 0.60$, which is based on the actual count of male fans.
City Population: The probability is calculated as $\frac{30000}{100000} = 0.30$, which is based on the actual population data.

Step 3: Determine Empirical Situations

From the analysis, the situations that involve empirical probability are: