.) A recent report indicated a typical family of four spends $490 per month on f

Question

.) A recent report indicated a typical family of four spends $490 per month on food. Assue the distribution of food expenditures for a family of four follows the normal distribution, w a standard deviation of $90 per month. a. What percent of the families spend more than $30 but less than $490 per month o food? b. What percent of the families spend less than $430 per month on food? c. What percent spend between $430 and $600 per month on food? d. What percent spend between $500 and $600 per month on food?

Explanation / Answer

Ans:

a)

z(30)=(30-490)/90=-5.11

z(490)=0

P(-5.11<z<0)=P(z<0)-P(z<-5.11)=0.5-0=0.5

50%

b)

z(430)=(430-490)/90=-0.67

P(z<-0.67)=0.2514

25.14%

c)

z(430)=-0.67

z(600)=(600-490)/90=1.22

P(-0.67<=z<=1.22)=P(z<1.22)-P(z<-0.67)=0.8888-0.2514=0.6373

63.73%

d)

z(500)=(500-490)/90=0.11

z(600)=1.22

P(0.11<z<1.22)=P(z<1.22)-P(z<0.11)=0.8888-0.5438=0.3450

34.5%

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