The regional manager in Exercise 6.10 plans to evaluate the speed of services at five local franchises of the restaurant. For the fives serves, determine the probability that
a. None will receive a movie coupon
b. two of the five will receive a coupon
c. three of the five will receive a coupon
d. all five will receive a coupon
We do not have the data from exercise 6.10 to note the speeds of the servers or the criterion for receiving a movie coupon.
If you repost with the needed data, we would be more able to help you.
how you can use sampling distribution and the concept of Central Limit Theorem to apply information and make good predictions and estimations when you shop for a particular item or product?
From exercise 6.10, n = 5 and the probability of receiving a coupon is 0.60.
with n = 5 and p = 0.600000
x P( X = x)
0 0.0102
1 0.0768
2 0.2304
3 0.3456
4 0.2592
5 0.0778
To determine the probabilities in each case, we need to know some additional information: the total number of franchises and the probability of a single franchise receiving a movie coupon. Let's assume there are a total of 50 franchises and a probability of 0.2 for each franchise to receive a movie coupon.
a. Probability of none receiving a coupon:
To calculate this, we use the formula for the probability of an event not occurring. In this case, it means no franchise receiving a movie coupon. So, the probability of none of the five franchises receiving a coupon is given by:
Probability = (1 - Probability of receiving a coupon)^Number of franchises
Probability of none receiving a coupon = (1 - 0.2)^5 = 0.32768
b. Probability of two franchises receiving a coupon:
To calculate this, we need to determine the number of ways we can choose two franchises out of the five that will receive a movie coupon. The probability of two franchises receiving a coupon out of five can be calculated using the binomial probability formula.
Probability = (Number of ways to choose k successes) * (Probability of success)^k * (Probability of failure)^(Number of trials - k)
In this case, the number of ways to choose two out of five is given by the binomial coefficient (5C2).
Probability of two franchises receiving a coupon = (5C2) * (0.2^2) * (0.8^3) = 0.2048
c. Probability of three franchises receiving a coupon:
Using a similar approach as in part b, but now with three successes out of five trials:
Probability of three franchises receiving a coupon = (5C3) * (0.2^3) * (0.8^2) = 0.0512
d. Probability of all five franchises receiving a coupon:
Again, using the binomial probability formula for five successes out of five trials:
Probability of all five franchises receiving a coupon = (5C5) * (0.2^5) * (0.8^0) = 0.00032
Please note that the probabilities may change depending on the number of franchises and the probability of receiving a movie coupon. Adjust the values in the calculations accordingly.