question 25 points 3

assume that adults have iq scores that are normally distributed with a mean of 98 and standard deviation of 15. find the probability that a randomly selected adult has an iq greater than 104.

0.3446
0.6723

Question

question 25 points 3

assume that adults have iq scores that are normally distributed with a mean of 98 and standard deviation of 15. find the probability that a randomly selected adult has an iq greater than 104.

0.3446
0.6723

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 parameters Using the *Normal Distribution Properties* knowledge point $$ \begin{aligned} &\mu = 98\ &\sigma = 15\ &X \sim N(98, 15^2)\ &\text{Target: } P(X > 104) \end{aligned} $$ ## Calculate the Z-score Using the *Z-score Calculation* knowledge point $$ \begin{aligned} &z = \frac{x - \mu}{\sigma}\ &z = \frac{104 - 98}{15} = \frac{6}{15} = 0.4 \end{aligned} $$ ## Find the probability Using the *Standard Normal Table* knowledge point $$ \begin{aligned} &P(X > 104) = P(Z > 0.4)\ &P(Z > 0.4) = 1 - \Phi(0.4)\ &\Phi(0.4) = 0.6554\ &P(Z > 0.4) = 1 - 0.6554 = 0.3446 \end{aligned} $$

(A) 0.3446

(B) 0.6723

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Question

Explanation:

Identify parameters

Calculate the Z-score

Find the probability

Answer: