a) "\\frac{\\Phi{\\frac{65,000-55,000}{4,500}}-\\Phi{\\frac{50,000-55,000}{4,500}}}{2}=\\frac{0.9736+0.733}{2}=0.8533"
the probability is 85.33%
b) "1-\\Phi{\\frac{70,000-55,000}{4,500}}=0.0009=0.09\\%"
c) "1-\\Phi{\\frac{x-55,000}{4,500}}=0.05"
"\\frac{x-55,000}{4,500}=1.96"
"x=63,820" - minimum income does a household need to earn to be in the top 5% of incomes
d) "\\Phi{\\frac{0-55,000}{4,500}}-\\Phi{\\frac{x-55,000}{4,500}}=0.3969"
"\\Phi{\\frac{x-55,000}{4,500}}=0.3969+0.5=0.8969"
"\\frac{x-55,000}{4,500}=1.63"
"x=47,665" maximum income does a household need to earn to be in the bottom 40% of incomes
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