a. "P(95<X<110)"
"P(95<X<110)=P(\\frac{95-100}{15}<Z<\\frac{110-100}{15})"
"=P(Z<0.6667)-P(Z< -0.3333)"
"=0.7475-0.3694=0.3781"
Thus, 37.81% of the population would obtain scores between 95 and 110
b"P(<X)=0.5-0.25" to get the left value
"P(\\frac{X-100}{15})=0.25" X is less than 100
"P(Z<-y)=0.25"
"y=\\frac{X-100}{15}" from =NORM.S.INV(0.25) excel formula "y=-0.67448975"
thus "-0.67448975=\\frac{X-100}{15}"
"X=(-0.67448975\\times15)+100=89.88265"
The right limit is "(100-89.88265)+100=110.1173"
the interval {89.88,110.12} contains 50% of the population and is centered at a score of 100
c. P(>125)
"P(\\frac{125-100}{15})=P(Z>)=1.667=0.0478"
"2500\\times0.0478=119.5"
120 people out of 2500 will score above 125
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