Question

3.
a company surveyed 480 customers about their shopping preferences and demographics.
they found:

• 300 customers prefer online shopping
• 180 customers are under age 35
• 135 customers under age 35 prefer online shopping
• 155 customers age 35 and older prefer in - store shopping

1. create a complete two - way table showing age group vs. shopping preference.
2. among customers who prefer in - store shopping, how many are 35 or older? how many are under 35?

4.
100 students at a school were asked whether they liked physics, chemistry or biology best.
31 boys liked physics best.
29 girls liked biology best.
28 students liked chemistry best.
3/5 of the students were boys.
19 boys liked chemistry best.
(a) use the information to complete the two - way table below.

	biology	chemistry	physics	total
girls
total

Explanation:

Problem 3 (Sub - question 1: Create two - way table)

Step 1: Determine the number of customers in each age group

We know that the total number of customers \(N = 480\). The number of customers under age 35 is \(n_{<35}=180\), so the number of customers age 35 and older is \(n_{\geq35}=480 - 180=300\).

Step 2: Determine the number of customers with each shopping preference

The number of customers who prefer online shopping is \(n_{online}=300\), so the number of customers who prefer in - store shopping is \(n_{in - store}=480 - 300 = 180\).

Step 3: Fill in the number of customers under age 35 for each shopping preference

We know that 135 customers under age 35 prefer online shopping. So the number of customers under age 35 who prefer in - store shopping is \(180-135 = 45\).

Step 4: Fill in the number of customers age 35 and older for each shopping preference

We know that 155 customers age 35 and older prefer in - store shopping. So the number of customers age 35 and older who prefer online shopping is \(300 - 155=145\).

Now we can create the two - way table:

Age Group / Shopping Preference	Online Shopping	In - Store Shopping	Total
35 and Older	145	155	300
Total	300	180	480

Step 5 (Sub - question 2 of Problem 3: In - store shopping by age)

From the two - way table, among customers who prefer in - store shopping (total of 180), the number of customers who are 35 or older is 155, and the number of customers who are under 35 is 45.

Problem 4 (Sub - question (a): Complete two - way table)

Step 1: Determine the number of boys and girls

We know that the total number of students \(N = 100\). The fraction of boys is \(\frac{3}{5}\), so the number of boys \(n_{boys}=\frac{3}{5}\times100 = 60\), and the number of girls \(n_{girls}=100 - 60 = 40\).

Step 2: Fill in the number of boys for each subject preference

• We know that 31 boys liked Physics best and 19 boys liked Chemistry best. Let the number of boys who liked Biology best be \(x\). Since the total number of boys is 60, we have \(x+19 + 31=60\), so \(x=60-(19 + 31)=10\).
• Number of boys who like Chemistry: 19 (given)
• Number of boys who like Physics: 31 (given)

Step 3: Fill in the number of girls for each subject preference

• We know that 29 girls liked Biology best. The total number of students who liked Chemistry best is 28, and 19 boys liked Chemistry best, so the number of girls who liked Chemistry best is \(28 - 19=9\).
• Let the number of girls who liked Physics best be \(y\). The total number of girls is 40, so \(y+9 + 29=40\), so \(y=40-(9 + 29)=2\).

Step 4: Fill in the total for each subject preference

• For Biology: Total number of students who liked Biology best is \(10 + 29=39\)
• For Chemistry: 28 (given)
• For Physics: \(31+2 = 33\)

The completed two - way table is:

/ Subject Preference	Biology	Chemistry	Physics	Total
Girls	29	9	2	40
Total	39	28	33	100

Problem 3 (Sub - question 2: In - store shopping by age)

From the two - way table we created in sub - question 1 of Problem 3:

• The number of customers who prefer in - store shopping and are 35 or older is 155.
• The number of customers who prefer in - store shopping and are under 35 is 45.

Answer:

s:

Problem 3

Sub - question 1:

The two - way table is:

Age Group / Shopping Preference	Online Shopping	In - Store Shopping	Total
35 and Older	145	155	300
Total	300	180	480

Sub - question 2:

Among customers who prefer in - store shopping, the number of customers who are 35 or older is 155, and the number of customers who are under 35 is 45.

Problem 4 (Sub - question (a))

The completed two - way table is:

/ Subject Preference	Biology	Chemistry	Physics	Total
Girls	29	9	2	40
Total	39	28	33	100