gaokao 2019 Q17

gaokao · China · national-III-science_gkztc 12 marks Data representation
17. (12 points) To understand the residual levels of two types of ions in mice, the following experiment was conducted: 200 mice were randomly divided into groups A and B, with 100 mice in each group. Group A mice were given a solution of ion type 甲, and group B mice were given a solution of ion type 乙. Each mouse was given the same volume of solution with the same molar concentration. After a period of time, a scientific method was used to measure the percentage of ions remaining in the mice's bodies. Based on the experimental data, the following histograms were obtained: [Figure]
Let $C$ be the event: ``the residual percentage of ion 乙 in the body is not less than 5.5''. Based on the histogram, the estimated value of $P ( C )$ is 0.70.
(1) Find the values of $a$ and $b$ in the histogram for the residual percentage of ion 乙;
(2) Estimate the mean residual percentage for ions 甲 and 乙 respectively (use the midpoint of each interval as the representative value for data in that interval).
Solution:
17. (12 points)\\
To understand the residual levels of two types of ions in mice, the following experiment was conducted: 200 mice were randomly divided into groups A and B, with 100 mice in each group. Group A mice were given a solution of ion type 甲, and group B mice were given a solution of ion type 乙. Each mouse was given the same volume of solution with the same molar concentration. After a period of time, a scientific method was used to measure the percentage of ions remaining in the mice's bodies. Based on the experimental data, the following histograms were obtained:\\
\includegraphics[max width=\textwidth, alt={}, center]{35e1ed43-6f5c-4d51-99b3-11f2215f3817-05_479_1479_246_322}

Let $C$ be the event: ``the residual percentage of ion 乙 in the body is not less than 5.5''. Based on the histogram, the estimated value of $P ( C )$ is 0.70.\\
(1) Find the values of $a$ and $b$ in the histogram for the residual percentage of ion 乙;\\
(2) Estimate the mean residual percentage for ions 甲 and 乙 respectively (use the midpoint of each interval as the representative value for data in that interval).\\