A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y , respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is f(x, y) = C(x + 2y) if 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, f(x, y) = 0 else.
(a) Determine the value of C. ANSWER: C=2/3
(b) Find the marginal distribution of X, that is, find the probability density function fX for X. ANSWER: 2/3(X+1)
*(c) Compute the expectation and variance of X.
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A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected...
Question 17 10 pts Determine the value of c such that f(x, y) is a valid joint pmf of the random variables X and Y, given the values for the joint pmf below Y-2 Y 4 Y=6 X-1 0.05 0.01 0.13 X-2 0.10 0.08 0.04 X -3 0.05 0.13 C OD.41 O O.82 O 0.14 O 0.07 Question 18 10 pts Aprivately owned liquor store operates botha drive-in facility and a walk-in facility. On a randomly selected day, let Xand...
7. A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the pro- portion of time that the second line is in use. Suppose that the joint probability density function for (X,Y) is f(tv) = ( +y), if 0 <r,y<1. elsewhere. (a) Compute the probability that neither line is busy more than half the time. (b) Determine whether or not...
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
please help. thank u The mean waiting time at the drive-through of a fast food restaurant from the time an orders placed to the time the order is received is 84 2 seconds. A manager devises a new drive through system that the believes will decrease wait time As a test the initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right...
Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 90% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner; then do the same for Restaurant Y. Compare the results.LOADING... Click the icon to view the data on drive-through service times.
6. The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease the wait time. He initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are in the following table: 108.5 67.4 58.0 75.9 65.1 80.4 95.5 86.3 70.9 72.0...
Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 99% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner, then do the same for Restaurant Y. Compare the results.
In a study of the accuracy of fast food drive-through orders, Restaurant A had345 accurate orders and 69 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.156 less than 0.209
In a study of the accuracy of fast food drive-through orders, Restaurant A had 300 accurate orders and 51 that were not accurate. a. Construct a 95% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 95% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.121<p<0.205. What do you conclude?
1. At a fast food restaurant, the waiting time at the drive-through window has an average of 3 minutes, with a standard deviation of 0.8 minutes. i. What is the probability that a random sample of 64 cars will have an average waiting time of less than 3.25 minutes? ii. Did you use the CLT to do this problem? Explain.