question 38 points 3

if $x$ follows a normal distribution with $\mu = 90$ and $\sigma = 20$, what is the probability that $x 80$?

0.6915
0.4988

Question

question 38 points 3

if $x$ follows a normal distribution with $\mu = 90$ and $\sigma = 20$, what is the probability that $x > 80$?

0.6915
0.4988

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": [ "Z-score Calculation", "Standard Normal Table", "Normal Distribution Properties" ], "new_concepts": [], "current_concepts": [ "Z-score Calculation", "Standard Normal Table", "Normal Distribution Properties" ] } ## Calculate the Z-score Using the *Z-score Calculation* knowledge point $$ z = \frac{X - \mu}{\sigma} = \frac{80 - 90}{20} = -0.5 $$ ## Find the cumulative probability Using the *Standard Normal Table* and *Normal Distribution Properties* knowledge points $$ \begin{aligned} P(X > 80) &= P(Z > -0.5) \ &= 1 - P(Z \le -0.5) \ &= 1 - 0.3085 \ &= 0.6915 \end{aligned} $$

(A) 0.6915

(B) 0.4988

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QUESTION IMAGE

Question

Explanation:

Calculate the Z-score

Find the cumulative probability

Answer: