question 6 points 3

$x$ follows a normal distribution with $\mu = 50$ and $\sigma = 4$. what is the probability that $x 43$?

4.01%
95.99%

Question

question 6 points 3

$x$ follows a normal distribution with $\mu = 50$ and $\sigma = 4$. what is the probability that $x > 43$?

4.01%
95.99%

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" ], "new_concepts": [], "current_concepts": [ "Normal Distribution Properties", "Z-score Calculation", "Standard Normal Table", "Interval Probability" ] } ## Identify the given parameters Using the *Normal Distribution Properties* knowledge point $$ \begin{aligned} &X \sim N(\mu, \sigma^2)\ &\mu = 50\ &\sigma = 4\ &\text{Target: } P(X > 43) \end{aligned} $$ ## Calculate the Z-score Using the *Z-score Calculation* knowledge point $$ Z = \frac{X - \mu}{\sigma} = \frac{43 - 50}{4} = -1.75 $$ ## Find the cumulative probability Using the *Standard Normal Table* knowledge point $$ \begin{aligned} &P(Z < -1.75) = 0.0401\ &P(Z < -1.75) = 4.01\% \end{aligned} $$ ## Calculate the target probability Using the *Interval Probability* knowledge point $$ \begin{aligned} P(X > 43) &= P(Z > -1.75)\ &= 1 - P(Z < -1.75)\ &= 1 - 0.0401\ &= 0.9599\ &= 95.99\% \end{aligned} $$

4.01%

95.99%

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Calculate the Z-score

Find the cumulative probability

Calculate the target probability

Answer: