Question #339831

2.) Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100.




a. What is the minimum score necessary to be in the top 15% of the SAT distribution?




b. Find the range of scores that defines the middle 80% of the distribution of SAT scores.




3. )The government would like to conduct a subsidy program for the lowest 5 percent of the families in terms of income. The government gathered data about family income and it’s found to be normally distributed with a mean of Php 130 000 and a standard deviation of Php 50 000. What is the cutoff income for the government program?


1
Expert's answer
2022-05-13T13:47:24-0400

2.)

a)


P(Xx)=10.15P(X\le x)=1-0.15

P(Zx500100)=0.85P(Z\le \dfrac{x-500}{100})=0.85

x500100=1.036433\dfrac{x-500}{100}=1.036433

x=603.64x=603.64

Minimum score is 603.64

b)


P(X<x1)=0.1P(X<x_1)=0.1

P(Z<x1500100)=0.1P(Z< \dfrac{x_1-500}{100})=0.1

x1500100=1.28155\dfrac{x_1-500}{100}=-1.28155

x1=371.845x_1=371.845

x2500100=1.28155\dfrac{x_2-500}{100}=1.28155

x2=628.155x_2=628.155

P(371.845X628.155)=0.8P(371.845\le X\le 628.155)=0.8

3.)



P(X<x)=0.05P(X<x)=0.05

P(Z<x13000050000)=0.05P(Z< \dfrac{x-130000}{50000})=0.05

x13000050000=1.6449\dfrac{x-130000}{50000}=-1.6449

x=47755x=47755


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