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There is a 0.6% chance that a randomly selected person has an IQ below 90.

What Is the Probability That a Randomly Selected Person Has an IQ Below 90?

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Question: The Stanford-Binet IQ Test is a normal curve with a mean of 100 and a standard deviation of 20. Estimate the probability that a randomly selected person has an IQ below 90?

Asked by kimberly

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To estimate the probability that a randomly selected person has an IQ below 90 using the Stanford-Binet IQ Test distribution, you can use the properties of the normal distribution. Here are the steps involved: 1. **Find the Z-score**: The Z-score indicates how many standard deviations away a particular score is from the mean. You can calculate it using the formula: \[ Z = \frac{(X - \mu)}{\sigma} \] where \(X\) is the score (90 in this case), \(\mu\) is the mean (100), and \(\sigma\) is the standard deviation (20). 2. **Calculate the Z-score for 90**: \[ Z = \frac{(90 - 100)}{20} = \frac{-10}{20} = -0.5 \] 3. **Consult the Z-table**: The Z-table (also known as the standard normal distribution table) provides the probability that a standard normal variable is less than or equal to a given value. For a Z-score of -0.5, you can look it up in the Z-table. The value corresponding to -0.5 is approximately 0.3085. This means that the probability of a randomly selected person having an IQ below 90 is approximately **0.3085** or **30.85%**. So, there is about a 30.85% chance that a randomly selected person will have an IQ below 90.

Answered by gpt-4o

Aug. 27, 2024, 2:06 p.m.

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To estimate the probability that a randomly selected person has an IQ below 90, we can use the z-score formula and a standard normal distribution table. Here's how: 1. Calculate the z-score: z = (X - μ) / σ, where X is the IQ score (90 in this case), μ is the mean (100), and σ is the standard deviation (20). z = (90 - 100) / 20 z = -10 / 20 z = -0.5 2. Look up the z-score (-0.5) in a standard normal distribution table or use a calculator that provides this information. The table will give you the area to the left of the z-score, which represents the probability of obtaining a value lower than the given z-score. The probability you find in the table for a z-score of -0.5 is approximately 0.3085, which means there is a 30.85% chance that a randomly selected person has an IQ below 90. Please keep in mind that the values presented above are only estimates and should not be taken as exact probabilities.

Answered by gpt-4

June 21, 2023, 5 p.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user kimberly's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Wednesday, June 21, 2023

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