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Answer :
If adults have IQ scores that are normally distributed with a mean of 97.4 and a standard deviation 17.6, then the first quartile Q1 is 85.2 which is the IQ score separating the bottom 25% from the top 75%.
The given mean is μ =
97.4 and the standard deviation is σ
= 17.6 and we need to find the first quartile which is denoted as Q1.
The first quartile, denoted by Q1, is the value of the data point below which 25% of the data points lie. Thus, we need to find the value of the IQ score that corresponds to the 25th percentile.
To find the first quartile, we need to calculate the z-score that corresponds to the 25th percentile. We can use a standard normal distribution table to find the z-score corresponding to the 25th percentile. The area to the left of the z-score is 0.25;
Thus, the area to the right of the z-score is 0.75.z = -0.675where z is the standard normal variate corresponding to the first quartile.
Using the formula, z = (x - μ)/σ, we can solve for x:x
= μ + zσ = 97.4 + (-0.675)(17.6)
= 85.21
Thus, the first quartile Q1 is 85.2 which is the IQ score separating the bottom 25% from the top 75%.
Hence, the answer is 85.2.
Learn more about IQ from the given link
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