QuestionHow many students have IQs > 100? Also, what % of a sample is within one standard deviation below the mean?
Studdy Solution
STEP 1
Assumptions1. The IQ scores are normally distributed.
. The mean IQ score is100.
3. The standard deviation of IQ scores is15.
4. The empirical rule applies, which states that approximately68% of data falls within one standard deviation of the mean,95% within two standard deviations, and99.7% within three standard deviations.
STEP 2
To solve Problem24, we need to find the percentage of students who have IQ scores above100. Since the mean IQ score is100, we are looking for the percentage of students who fall more than one standard deviation above the mean.
STEP 3
According to the empirical rule, approximately50% of students will have IQ scores above the mean (100).
STEP 4
The empirical rule also states that approximately34% of students will have IQ scores within one standard deviation above the mean.
STEP 5
Subtract the percentage of students within one standard deviation above the mean from the percentage of students above the mean to find the percentage of students with IQ scores above100.
STEP 6
Calculate the percentage of students with IQ scores above100.
Approximately16% of students will have IQs above100.
STEP 7
To solve Problem26, we need to find the percentage of students who fall within one standard deviation below the mean.
STEP 8
According to the empirical rule, approximately34% of students will have IQ scores within one standard deviation below the mean.So, approximately34% of a sample will fall within one standard deviation below the mean.
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