The 24 students in Ms.Cleary's homeroom are surveyed. They are asked which of the several prices they pay for a ticket to the school fasion show
Results:
$1.00-20
$1.50-20
$2.00-18
$2.50-15
$3.00-12
$3.50-10
$4.00-8
$4.50-7
A. There are 480 students in the school. Use the data from Ms. Cleary's class to predict ticket sales for the entire school for each price.
B. Use your results from part (a). For each price, find the school's projected income from ticket sales
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To find the projected ticket sales for the entire school for each price, you can follow these steps:
A. Predicted ticket sales for each price:
1. Calculate the percentage of students in Ms. Cleary's homeroom who paid each price by dividing the number of students who paid that price by the total number of students in the class (24).
- For example, for $1.00: 20/24 = 0.8333 = 83.33%
2. Multiply the percentage from Step 1 by the total number of students in the school (480).
- For example, for $1.00: 83.33% * 480 = 399.98 ≈ 400 students
3. Repeat Steps 1 and 2 for each price to get the predicted ticket sales for the entire school.
B. Projected income from ticket sales:
4. Multiply the predicted ticket sales for each price by the price itself to get the projected income from ticket sales.
- For example, at $1.00: 400 * $1.00 = $400
5. Repeat Step 4 for each price to get the school's projected income from ticket sales for each price.
Here is the breakdown for each step:
A. Predicted ticket sales for each price:
- $1.00: (20/24) * 480 = 400 students
- $1.50: (20/24) * 480 = 400 students
- $2.00: (18/24) * 480 = 360 students
- $2.50: (15/24) * 480 = 300 students
- $3.00: (12/24) * 480 = 240 students
- $3.50: (10/24) * 480 = 200 students
- $4.00: (8/24) * 480 = 160 students
- $4.50: (7/24) * 480 = 140 students
B. Projected income from ticket sales:
- $1.00: 400 * $1.00 = $400
- $1.50: 400 * $1.50 = $600
- $2.00: 360 * $2.00 = $720
- $2.50: 300 * $2.50 = $750
- $3.00: 240 * $3.00 = $720
- $3.50: 200 * $3.50 = $700
- $4.00: 160 * $4.00 = $640
- $4.50: 140 * $4.50 = $630
Therefore, the projected ticket sales for the entire school and the projected income from ticket sales for each price are as follows:
A. Projected ticket sales for the entire school:
- $1.00: 400 students
- $1.50: 400 students
- $2.00: 360 students
- $2.50: 300 students
- $3.00: 240 students
- $3.50: 200 students
- $4.00: 160 students
- $4.50: 140 students
B. Projected income from ticket sales:
- $1.00: $400
- $1.50: $600
- $2.00: $720
- $2.50: $750
- $3.00: $720
- $3.50: $700
- $4.00: $640
- $4.50: $630
To predict ticket sales for the entire school and the projected income, we can use the data from Ms. Cleary's class as a representative sample of the entire school.
A. To predict ticket sales for each price at the entire school, we need to find the proportion of students in Ms. Cleary's class who paid each price and then apply that proportion to the total number of students in the school. Here's how to do it:
Step 1: Calculate the proportion for each price in Ms. Cleary's class:
- For $1.00: 20/24 = 0.8333 (rounded to 4 decimal places)
- For $1.50: 20/24 = 0.8333
- For $2.00: 18/24 = 0.7500
- For $2.50: 15/24 = 0.6250
- For $3.00: 12/24 = 0.5000
- For $3.50: 10/24 = 0.4167 (rounded to 4 decimal places)
- For $4.00: 8/24 = 0.3333 (rounded to 4 decimal places)
- For $4.50: 7/24 = 0.2917 (rounded to 4 decimal places)
Step 2: Multiply each proportion by the total number of students in the school (480) to get the projected ticket sales for each price:
- For $1.00: 0.8333 * 480 = 399.98 (rounded to 2 decimal places)
- For $1.50: 0.8333 * 480 = 399.98 (rounded to 2 decimal places)
- For $2.00: 0.7500 * 480 = 360.00
- For $2.50: 0.6250 * 480 = 300.00
- For $3.00: 0.5000 * 480 = 240.00
- For $3.50: 0.4167 * 480 = 200.02 (rounded to 2 decimal places)
- For $4.00: 0.3333 * 480 = 159.98 (rounded to 2 decimal places)
- For $4.50: 0.2917 * 480 = 140.01 (rounded to 2 decimal places)
B. To find the school's projected income from ticket sales, we need to multiply the projected ticket sales for each price by the corresponding price and then sum them up. Here's how to do it:
Step 1: Multiply each projected ticket sales by the price:
- For $1.00: 399.98 * 1 = 399.98 (rounded to 2 decimal places)
- For $1.50: 399.98 * 1.5 = 599.97 (rounded to 2 decimal places)
- For $2.00: 360 * 2 = 720
- For $2.50: 300 * 2.5 = 750
- For $3.00: 240 * 3 = 720
- For $3.50: 200.02 * 3.5 = 700.07 (rounded to 2 decimal places)
- For $4.00: 159.98 * 4 = 639.92 (rounded to 2 decimal places)
- For $4.50: 140.01 * 4.5 = 630.04 (rounded to 2 decimal places)
Step 2: Sum up the projected incomes from each price:
399.98 + 599.97 + 720 + 750 + 720 + 700.07 + 639.92 + 630.04 = 4960.9 (rounded to 1 decimal place)
Therefore, the school's projected income from ticket sales is approximately $4960.9.