select the correct answer from the drop-down menu.

the mean of the scores obtained by a class of students on a physics test is 42. the standard deviation is 8. students have to score at least 50 to pass the test.

assuming that the data is normally distributed, approximately choose an answer % of the students passed the test.

options:
8
16
34
84

Question

select the correct answer from the drop-down menu.

the mean of the scores obtained by a class of students on a physics test is 42. the standard deviation is 8. students have to score at least 50 to pass the test.

assuming that the data is normally distributed, approximately choose an answer % of the students passed the test.

options:
8
16
34
84

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Normal Distribution Calculations", "Z-Score Calculation", "Empirical Rule" ], "new_concepts": [], "current_concepts": [ "Normal Distribution Calculations", "Z-Score Calculation", "Empirical Rule" ] } ## Calculate the z-score for the passing threshold $$ \begin{aligned} &\mu = 42,\quad \sigma = 8,\quad X = 50\ &z = \frac{X - \mu}{\sigma} = \frac{50 - 42}{8} = 1 \end{aligned} $$ ## Determine the percentage of students passing using the Empirical Rule $$ \begin{aligned} &P(Z \ge 1) = 0.5 - P(0 \le Z \le 1)\ &P(0 \le Z \le 1) \approx 0.34\ &P(Z \ge 1) \approx 0.50 - 0.34 = 0.16 = 16\% \end{aligned} $$

8

16

34

84

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Normal Distribution Calculations" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the z-score for the passing threshold

Determine the percentage of students passing using the Empirical Rule

Answer: