Question
A company surveys
200
200 shoppers to find out what type of bottled water they prefer.The partial two-way table shown gives the results of the survey as relative frequencies.
bottled water
purified water mineral water total
men 0.28 0.13 0.41
women 0.14 ? 0.59
total 0.42 0.58 1
A. What is the missing value in the table?
B. Based on the results in the table, how many shoppers are men who prefer mineral water?
A
.
A.
B
.
B.
Answers
GPT-4o mini
To solve the problem, let's first look at the partial two-way table provided:
| | Purified Water | Mineral Water | Total |
|----------------|----------------|---------------|--------|
| Men | 0.28 | 0.13 | 0.41 |
| Women | 0.14 | ? | 0.59 |
| Total | 0.42 | 0.58 | 1 |
**A. What is the missing value in the table?**
To find the missing value for women who prefer mineral water, we can use the information from the total relative frequencies.
From the total relative frequencies:
- Total for Purified Water (0.42) = Men (0.28) + Women (0.14)
- Total for Mineral Water (0.58) = Men (0.13) + Women (?).
- Since the total for Women is 0.59, we can calculate:
\[
\text{Women (Mineral Water)} = \text{Total (Women)} - \text{Women (Purified Water)}
= 0.59 - 0.14 = 0.45
\]
So, the missing value in the table is 0.45.
**A.** The missing value in the table is **0.45**.
---
**B. Based on the results in the table, how many shoppers are men who prefer mineral water?**
To find the number of men who prefer mineral water, we'll first determine the total number of shoppers who participated in the survey and then apply the relative frequency for men who prefer mineral water.
There are 200 shoppers sampled. According to the provided table:
- The relative frequency for men who prefer mineral water is 0.13.
Now we can calculate the number of men who prefer mineral water:
\[
\text{Number of Men (Mineral Water)} = \text{Total Shoppers} \times \text{Relative Frequency (Men, Mineral Water)}
= 200 \times 0.13 = 26
\]
**B.** The number of shoppers who are men and prefer mineral water is **26**.
| | Purified Water | Mineral Water | Total |
|----------------|----------------|---------------|--------|
| Men | 0.28 | 0.13 | 0.41 |
| Women | 0.14 | ? | 0.59 |
| Total | 0.42 | 0.58 | 1 |
**A. What is the missing value in the table?**
To find the missing value for women who prefer mineral water, we can use the information from the total relative frequencies.
From the total relative frequencies:
- Total for Purified Water (0.42) = Men (0.28) + Women (0.14)
- Total for Mineral Water (0.58) = Men (0.13) + Women (?).
- Since the total for Women is 0.59, we can calculate:
\[
\text{Women (Mineral Water)} = \text{Total (Women)} - \text{Women (Purified Water)}
= 0.59 - 0.14 = 0.45
\]
So, the missing value in the table is 0.45.
**A.** The missing value in the table is **0.45**.
---
**B. Based on the results in the table, how many shoppers are men who prefer mineral water?**
To find the number of men who prefer mineral water, we'll first determine the total number of shoppers who participated in the survey and then apply the relative frequency for men who prefer mineral water.
There are 200 shoppers sampled. According to the provided table:
- The relative frequency for men who prefer mineral water is 0.13.
Now we can calculate the number of men who prefer mineral water:
\[
\text{Number of Men (Mineral Water)} = \text{Total Shoppers} \times \text{Relative Frequency (Men, Mineral Water)}
= 200 \times 0.13 = 26
\]
**B.** The number of shoppers who are men and prefer mineral water is **26**.