Questions: Consider how the following scenario could be modeled with a binomial distribution, and answer the question that follows. 54.4% of tickets sold to a movie are sold with a popcorn coupon, and 45.6% are not. You want to calculate the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets (or 6 successes in 10 trials). What value should you use for the parameter p?

Solution Steps

To solve this problem, we need to identify the parameter \( p \) for a binomial distribution. The parameter \( p \) represents the probability of success on a single trial. In this context, a "success" is defined as selling a ticket with a popcorn coupon. According to the problem, 54.4% of tickets are sold with a popcorn coupon. Therefore, the value of \( p \) is 0.544.

In this scenario, we define a "success" as selling a ticket with a popcorn coupon. The problem states that \( 54.4\% \) of tickets sold are with a popcorn coupon. Therefore, we can express the probability of success \( p \) as: \[ p = 0.544 \]

The value of \( p \) is directly derived from the percentage of tickets sold with a popcorn coupon. Thus, we have: \[ p = 0.544 \]

Final Answer