A regional manager visits local fast food franchises and evaluates the speed of the service. if the manager receives her meal within 45 seconds, the server is given a free movie-admission coupon. If it takes more than 45 seconds, the server receives nothing. Throughout the company's franchises, the probability is 0.60 that a meal will be served served within seconds. What is the expected number of coupons a counter employee will receive when serving the regional manager?
Number of meals served * .6 = ?
To find the expected number of coupons a counter employee will receive when serving the regional manager, we need to calculate the probability of receiving a coupon for each possible outcome.
Let's assume that X represents the number of coupons a counter employee receives. We can use the concept of expected value to calculate this. The formula for calculating the expected value is as follows:
E(X) = Σ(x * P(x))
Where E(X) represents the expected value, x represents the possible outcomes, and P(x) represents the probability associated with each outcome.
In this scenario, the possible outcomes are 0 coupons (X = 0) and 1 coupon (X = 1). Now, let's calculate the probabilities for each outcome.
The probability of receiving 0 coupons is the probability of the meal taking more than 45 seconds, which is (1 - 0.60) = 0.40.
The probability of receiving 1 coupon is the probability of the meal being served within 45 seconds, which is 0.60.
Now, let's substitute these values into the formula to calculate the expected value:
E(X) = (0 * 0.40) + (1 * 0.60)
= 0 + 0.60
= 0.60
Therefore, the expected number of coupons a counter employee will receive when serving the regional manager is 0.60 coupons.