Question

Edward Sayers has collected information showing that the average Amazon Prime customer spent $2,486 over the last twelve months compared to $544 for non-Prime Amazon customers. It is known that the amount spent by Amazon Prime customers is normally distributed, with a standard deviation of $125.

What is the probability that an Amazon Prime customer spent more than $2,771 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

ANSWER:

What is the probability that an Amazon Prime customer spent less than $2,301 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

ANSWER:

What is the probability that an Amazon Prime customer spent more than $2,206 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

ANSWER:

What percent of the Amazon Prime customers spent between $2,366 and $2,846 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.

ANSWER: %

What percent of the Amazon Prime customers spent less than $2,806 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.

ANSWER: %

Four percent of the Amazon Prime customers spent less than what amount over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.

ANSWER: $

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	2486
std deviation   =σ=	125

a)

probability that an Amazon Prime customer spent more than $2,771 over the last twelve months :

probability =P(X>2771)=P(Z>(2771-2486)/125)=P(Z>2.28)=1-P(Z<2.28)=1-0.9887=0.0113~ 1.13 %

b)

probability that an Amazon Prime customer spent less than $2,301 over the last twelve months :

probability =P(X<2301)=(Z<(2301-2486)/125)=P(Z<-1.48)=0.0694~ 6.94 %

c)

probability that an Amazon Prime customer spent more than $2,206 over the last twelve months :

probability =P(X>2206)=P(Z>(2206-2486)/125)=P(Z>-2.24)=1-P(Z<-2.24)=1-0.0125=0.9875~ 98.75 %

d)

What percent of the Amazon Prime customers spent between $2,366 and $2,846 over the last twelve months :

probability =P(2366<X<2846)=P((2366-2486)/125)<Z<(2846-2486)/125)=P(-0.96<Z<2.88)=0.998-0.1685=0.8295~82.95 %

e)

What percent of the Amazon Prime customers spent less than $2,806 over the last twelve months :

probability =P(X<2806)=(Z<(2806-2486)/125)=P(Z<2.56)=0.9948~ 99.48 %

f)

Four percent of the Amazon Prime customers spent less than what amount over the last twelve months :

for 4th percentile critical value of z=		-1.75
therefore corresponding value=mean+z*std deviation=			2267.25