Question

at a baseball game, approximately 33% are fans of the visiting team. the other attendees are fans of the home team. if 109 attendees are chosen at random, and assuming that the data follow a binomial probability model, how many of them would you expect to be fans of the home team? where applicable, please round your answer to one decimal place.

Explanation:

Step1: Find the probability of home team fans

The probability of visiting team fans is 33% or 0.33. So the probability of home team fans is $1 - 0.33 = 0.67$.

Step2: Calculate the expected number

For a binomial distribution, the expected value (mean) is $n\times p$, where $n = 109$ (number of trials) and $p = 0.67$ (probability of success, here being a home team fan). So we calculate $109\times0.67$.
$109\times0.67 = 73.03$

Step3: Round to one decimal place

Rounding 73.03 to one decimal place gives 73.0.

Answer:

73.0