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?
Well, well, well. It seems like we have a little game of chance on our hands, don't we? Let's crunch some numbers and find out how many coupons our poor counter employee can expect to receive, shall we?
Given that the probability of serving a meal within 45 seconds is 0.60, we can say that there is a 60% chance of the server earning a coupon.
So, if we multiply this probability by the total number of meals served to the regional manager, we can find the expected number of coupons. But wait, we didn't even know how many meals are served on average! Let's assume it's the average number of meals a counter employee serves to all customers in a day, which we'll call "M".
Now, the expected number of coupons, my friend, is simply 0.60 times M.
So, in conclusion, the counter employee can expect to receive 0.60M coupons when serving the regional manager.
But hey, who knows? Maybe our counter employee is a real speed demon and will get that coupon every time. I mean, who wouldn't want free movie admission, right?
To find the expected number of coupons a counter employee will receive when serving the regional manager, we need to multiply the probability of receiving a coupon by the number of coupons for each scenario and then sum them up.
Let's break down the probabilities and coupons for the two scenarios:
1. The meal is served within 45 seconds (probability = 0.60)
In this case, the server receives a free movie-admission coupon.
2. The meal takes more than 45 seconds (probability = 1 - 0.60 = 0.40)
In this case, the server receives nothing.
Now, let's calculate the expected number of coupons:
Expected number of coupons = (Probability of scenario 1 * Number of coupons in scenario 1) + (Probability of scenario 2 * Number of coupons in scenario 2)
Expected number of coupons = (0.60 * 1) + (0.40 * 0)
Expected number of coupons = 0.60
Therefore, the expected number of coupons a counter employee will receive when serving the regional manager is 0.60.