find $p(x 80)$ if $x$ follows a normal distribution with a mean of 75 and a standard deviation of 5.

15.87%
54.29%

Question

find $p(x > 80)$ if $x$ follows a normal distribution with a mean of 75 and a standard deviation of 5.

15.87%
54.29%

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Normal Distribution Properties", "Z-score Calculation", "Standard Normal Table" ], "new_concepts": [], "current_concepts": [ "Normal Distribution Properties", "Z-score Calculation", "Standard Normal Table" ] } ## Identify given parameters Using the *Normal Distribution Properties* knowledge point $$ \begin{aligned} &\mu = 75\ &\sigma = 5\ &X \sim N(75, 5^2) \end{aligned} $$ ## Calculate the Z-score Using the *Z-score Calculation* knowledge point $$ \begin{aligned} &x = 80\ &z = \frac{x - \mu}{\sigma} = \frac{80 - 75}{5} = 1 \end{aligned} $$ ## Find the probability Using the *Standard Normal Table* knowledge point $$ \begin{aligned} &P(X > 80) = P(Z > 1)\ &P(Z > 1) = 1 - P(Z \le 1) = 1 - 0.8413 = 0.1587\ &P(X > 80) = 15.87\% \end{aligned} $$

(A) 15.87%

(B) 54.29%

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QUESTION IMAGE

Question

Explanation:

Identify given parameters

Calculate the Z-score

Find the probability

Answer: