Questions: Random Variables and Distributions Making predictions using experimental data for compound events Silve A school gave some of its students an assessment on two subjects: language and math. Each student's score was classified as at grade level, above grade level, or below grade level for each subject. Here is a summary of the data the school got after assessing 225 students. Language Math Number of students --- --- --- at grade level at grade level 14 at grade level above grade level 26 at grade level below grade level 39 above grade level at grade level 19 above grade level above grade level 18 above grade level below grade level 23 below grade level at grade level 37 below grade level above grade level 27 below grade level below grade level 22 Suppose the school will assess 150 more students. How many of these 150 students will score below grade level in exactly one subject? Use the data to make a prediction.

Random Variables and Distributions
Making predictions using experimental data for compound events
Silve

A school gave some of its students an assessment on two subjects: language and math. Each student's score was classified as at grade level, above grade level, or below grade level for each subject.

Here is a summary of the data the school got after assessing 225 students.

Language  Math  Number of students
---  ---  ---
at grade level  at grade level  14
at grade level  above grade level  26
at grade level  below grade level  39
above grade level  at grade level  19
above grade level  above grade level  18
above grade level  below grade level  23
below grade level  at grade level  37
below grade level  above grade level  27
below grade level  below grade level  22

Suppose the school will assess 150 more students.
How many of these 150 students will score below grade level in exactly one subject? Use the data to make a prediction.
Transcript text: Random Variables and Distributions Making predictions using experimental data for compound events Silve A school gave some of its students an assessment on two subjects: language and math. Each student's score was classified as at grade level, above grade level, or below grade level for each subject. Here is a summary of the data the school got after assessing 225 students. \begin{tabular}{|c|c|c|} \hline Language & Math & \begin{tabular}{c} Number of \\ students \end{tabular} \\ \hline at grade level & at grade level & 14 \\ \hline at grade level & above grade level & 26 \\ \hline at grade level & below grade level & 39 \\ \hline above grade level & at grade level & 19 \\ \hline above grade level & above grade level & 18 \\ \hline above grade level & below grade level & 23 \\ \hline below grade level & at grade level & 37 \\ \hline below grade level & above grade level & 27 \\ \hline below grade level & below grade level & 22 \\ \hline \end{tabular} Suppose the school will assess 150 more students. How many of these 150 students will score below grade level in exactly one subject? Use the data to make a prediction. $\square$
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Solution

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Solution Steps

To predict how many of the 150 students will score below grade level in exactly one subject, we first need to calculate the probability of a student scoring below grade level in exactly one subject based on the given data. This involves finding the total number of students who scored below grade level in exactly one subject and dividing it by the total number of students assessed. Then, we multiply this probability by 150 to get the expected number of students.

Step 1: Calculate the Number of Students Scoring Below Grade Level in Exactly One Subject

To find the number of students who scored below grade level in exactly one subject, we sum the relevant categories from the data:

  • Language at grade level & Math below grade level: 39 students
  • Language above grade level & Math below grade level: 23 students
  • Language below grade level & Math at grade level: 37 students
  • Language below grade level & Math above grade level: 27 students

Thus, the total number of students scoring below grade level in exactly one subject is: \[ 39 + 23 + 37 + 27 = 126 \]

Step 2: Calculate the Probability

The probability that a student scores below grade level in exactly one subject is given by the ratio of the number of such students to the total number of students assessed: \[ P(\text{below in one subject}) = \frac{126}{225} \approx 0.56 \]

Step 3: Predict the Number of Students for 150 New Assessments

To predict how many of the 150 new students will score below grade level in exactly one subject, we multiply the probability by 150: \[ \text{Predicted number} = 0.56 \times 150 = 84 \]

Final Answer

\(\boxed{84}\)

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