Thank you for visiting Assume that adults have IQ scores that are normally distributed with a mean of 100 2 and a standard deviation of 19 5 Find the. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
To calculate the probability that a randomly selected adult has an IQ greater than 131.9, first find the z-score using the formula z = (X - μ) / σ, then use the standard normal distribution table to find the corresponding probability.
Explanation:
The student's question pertains to finding the probability that a randomly selected adult has an IQ score greater than 131.9, given that IQ scores are normally distributed with a mean (μ) of 100.2 and a standard deviation (σ) of 19.5. The calculation of this probability involves finding the z-score and then using the standard normal distribution table to find the corresponding probability.
To find the z-score, we use the formula: z = (X - μ) / σ, where X is the value in question (131.9 in this case). Plugging in the values, we get z = (131.9 - 100.2) / 19.5.
Once the z-score is calculated, consult the standard normal distribution table (or a calculator with the normal distribution function) to find the area to the right of this z-score, which represents the probability that a randomly selected adult has an IQ greater than 131.9. Since tables typically give the area to the left, you will need to subtract this value from 1 to obtain the probability we're looking for. Remember to round the result to four decimal places as needed.
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