3. Your mail-order company advertises that it ships 90% ofits orders withintree

Question

3. Your mail-order company advertises that it ships 90% ofits orders withintree working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit. a. What is the mean of the sampling distribution of p? b. Find the standard deviation of the sampling distribution of p. Check that the 10% condition is met c. Is the sampling distribution approximately Normal? Check that the Normal conditions are met. d. The audit reveals that 86 of theses orders were shipped on time (that is 86%). What is the probability that the proportion of on time orders is 86% or less?

Explanation / Answer

SolutionA:

mean=p^=90%=0.9

SolutionB:

std deviation=sqrt(p^(1-p^)/100)

=sqrt(0.9(1-0.9)/100

=0.03

10% condition:

np^=100*0.90=90

n(1-p^)=100*(1-0.9)=100*0.10=10

np^ and n(1-p^) are >=10

10% condition is met.

sOLUTIONC:

np^=100*0.90=90

n(1-p^)=100*(1-0.9)=100*0.10=10

np^ and n(1-p^) are >=10

10% condition is met.

SAMPLIMG DISTRIBUTION IS APPROXIMATELY NORMAL

Solutiond:

P(p^<0.86)

=P(z<0.86-0.90/0.03)

=P(Z<-1.33)

=1-p(Z<1.33)

=1-0.9082

=0.0918

ANSWER:0.0918

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