A new restaurant with 123 seats is being planned. Studies show that 63% of the customers demand a smoke free area. How many seats sould be in the non-smoking area in order to be very sure (mean+3StandardDeviation) of having enough seating there?
To determine the number of seats that should be in the non-smoking area to be very sure, we need to calculate the mean and standard deviation of the number of customers demanding a smoke-free area.
First, let's calculate the mean:
Mean = Total number of seats x Percentage of customers demanding a smoke-free area
Mean = 123 seats x 0.63
Mean = 77.49 (rounded to 77 seats)
Next, we need to calculate the standard deviation. Unfortunately, the question doesn't provide the specific standard deviation of the number of customers. We have two options here:
Option 1: If you have access to the actual standard deviation data for the number of customers demanding a smoke-free area, you can use that value to calculate the answer. In this case, you can proceed with the calculation.
Option 2: If you don't have access to the standard deviation data, you can make an assumption about a reasonable value to use. However, it's important to note that this assumption may not be accurate, and the true value might differ.
Let's assume a standard deviation value of 10 for this example.
Mean + (3 × Standard Deviation) = Seats in non-smoking area
Using the assumed standard deviation (10) and the calculated mean (77), we can calculate the number of seats in the non-smoking area.
77 + (3 × 10) = 77 + 30 = 107 seats
Therefore, to be very sure of having enough seating in the non-smoking area, you should allocate 107 seats in that area. Remember, this calculation assumes a standard deviation of 10, which may not be the actual value. If you have access to the actual standard deviation, you should use that instead.