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Intelligence Quotient (IQ) scores are widely used to measure cognitive ability. A psychological research institute analyzes IQ scores to understand population intelligence distributions. In 2023, the IQ scores of a large adult population were normally distributed with a mean of 100 and a standard deviation of 15.
Using this information, calculate the following probabilities or values for the IQ scores:
The percentage of adults with IQ scores between 85 and 100.
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\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
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\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
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\(C\)
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9
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\(\div\)
\(\tan{\,}\)
C
0
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+
-
=
\(\pourcent\)
The percentage of adults with IQ scores between 70 and 100.
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
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9
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→
\(\sin{\,}\)
4
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\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
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0
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+
-
=
\(\pourcent\)
The percentage of adults with IQ scores less than 115.
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\(x\)
\(n\)
\(u_n\)
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\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
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6
(
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\(\cos{\,}\)
1
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3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
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+
-
=
\(\pourcent\)
In 2024, if there were 800 adults in this population, estimate the number of adults with IQ scores greater than 130 (round to the nearest integer).
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
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6
(
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\(\cos{\,}\)
1
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3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
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+
-
=
adults
For a normal distribution, the coverage probabilities are illustrated below:
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