In a sample of 50 museum visitors one afternoon, 22 were female and 28 were male. If there were 800 museum visitors that afternoon, estimate the number of visitors who were female.
A. 220
B. 352
C. 448
D. 700
We can set up a proportion:
\begin{align*}
\frac{\text{number of female visitors}}{\text{total number of visitors}} &= \frac{22}{50} \\
\text{number of female visitors} &= \frac{22}{50} \cdot 800 \\
&= 352
\end{align*}
Therefore, the answer is $\boxed{\textbf{(B)}\ 352}$.
b?
Yes, you are correct. Thank you for letting me know. The answer is (B) 352.
A manufacturer samples 100 wires for quality testing. Four of the wires are found to be defective. If 750 wires are produced in one hour, how many should the manufacturer expect to be defective?
A. 30
B. 60
C. 75
D. 96
We can set up a proportion:
\begin{align*}
\frac{\text{number of defective wires}}{\text{total number of wires}} &= \frac{4}{100} \\
\text{number of defective wires} &= \frac{4}{100} \cdot 750 \\
&= 30
\end{align*}
Therefore, the answer is $\boxed{\textbf{(A)}\ 30}$.
The city of Valley Grove is considering shortening the length of the school day. The school board hired Mr. Kent to do a survey to help them decide what to do.
a. Mr. Kent interviewed 54 students as they left the school. Is this a random sample? Explain.
b. Mr. Kent used this survey question: “Should the lengthy school day, which now extends for 7.5 hours, be shortened to 6 hours?” Is this question biased or fair? Explain.
c. Of the 54 responses he received, 51 were “yes.” The rest were “no.” What percent of the responses were “no”?
a. It is not clear from the information given whether this is a random sample. We do not know how the 54 students were selected, or whether their responses are representative of the entire student population.
b. The question is biased because it contains persuasive language ("lengthy school day") that could influence the students' responses. It would be more fair to ask a more neutral question such as "Do you think the school day should be shortened?"
c. There were 54 - 51 = 3 responses that were "no." The percent of responses that were "no" is:
$$\frac{3}{54} \cdot 100\% \approx 5.6\%$$
Therefore, approximately 5.6% of the responses were "no."