The percentage of scores will fall between 85 and 115 is 68.26%
Given,
Scores on the Wechsler Adult Intelligence Scale (WAIS) are normally distributed with,
Mean = 100
Standard deviation = 15
We have to find the percentage of scores fall between 85 and 115.
That is,
P(85 < X < 115) = \ [tex]P[/tex] [tex](\frac{85-100}{15}[/tex] < [tex]\frac{x-mean}{standard deviation}[/tex] < [tex]\frac{115-100}{15}[/tex][tex])[/tex]
= P(-1 < Z < 1)
= \P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
\P(85 < X < 115) = 0.6826
The probability that a person would score between 85 and 115 is 0.6826
And, the percentage of scores will fall between 85 and 115 is 68.26%
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