Supplementary Exercise 6.62 The amount of sales tax paid on a purchase is rounde

Question

Supplementary Exercise 6.62

The amount of sales tax paid on a purchase is rounded to the nearest cent. Assume that the round-off error is uniformly distributed in the interval -.50 to .50 cents. (Round the intermediate calculations to 4 decimal places. Round your answers to 4 decimal places.)

The amount of sales tax paid on a purchase is rounded to the nearest cent. Assume that the round-off error is uniformly distributed in the interval -.50 to .50 cents. (Round the intermediate calculations to 4 decimal places. Round your answers to 4 decimal places.)

Explanation / Answer

Ans:

a)Given that

a=-0.5,b=0.5

f(x)=1/(b-a)=1/(0.5-(-0.5))=1 for -1<=x<=1

cumulative distribution function:

F(x)=P(X<=x)=(x-a)/(b-a)=(x-(-0.5))/(0.5-(-0.5)=x+0.5

c)

P(X<=-0.4 or X>=0.4)=P(X<=-0.4)+P(X>=0.4)

=(-0.4+0.5)+(1-(0.4+0.5))

=0.1+(1-0.9)=0.1+0.1=0.2

d)

P(X<=-0.1 or X>=0.1)=P(X<=-0.1)+P(X>=0.1)

=(-0.1+0.5)+(1-(0.1+0.5))

=0.4+(1-0.6)=0.4+0.4=0.8

e)mean=(a+b)/2=(-0.5+0.5)/2=0

standard deviation=sqrt((b-a)^2/12)=sqrt((0.5+0.5)^2/12)=0.289

f)

P(-0.289<=x<=0.289)=P(x<=0.289)-P(x<=-0.289)

=(0.289+0.5)-(-0.289+0.5)

=0.578

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.