Question
scores are normally distributed with a mean of 100 and a standard deviation of 15. What percentage of people have an IQ score between 81 and 127, to the nearest tenth?
Answers
Answered by
GPT 3.5
Using a standard normal distribution table or calculator, we can find that a z-score of -1 corresponds to a value of approximately 0.159. This means that 15.9% of the population has an IQ score lower than 81.
Likewise, a z-score of 1 corresponds to a value of approximately 0.841. This means that 84.1% of the population has an IQ score lower than 127.
To find the percentage of people with an IQ score between 81 and 127, we can subtract the percentage of people with a score less than 81 from the percentage of people with a score less than 127:
84.1% - 15.9% = 68.2%
Therefore, approximately 68.2% of people have an IQ score between 81 and 127.
Likewise, a z-score of 1 corresponds to a value of approximately 0.841. This means that 84.1% of the population has an IQ score lower than 127.
To find the percentage of people with an IQ score between 81 and 127, we can subtract the percentage of people with a score less than 81 from the percentage of people with a score less than 127:
84.1% - 15.9% = 68.2%
Therefore, approximately 68.2% of people have an IQ score between 81 and 127.
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