Question

Lego has found that the average time it takes to build its version of the Death Star from Star Wars follows a normal distribution with a mean of 27.13 hours with a standard deviation of

5.16 hours. Complete parts ​(a) through ​(f) below.

​a) What is the probability that it takes a Lego builder less than 20 hours to build the Death​ Star?

​(Round to four decimal​ places.)

​b) What is the probability that it takes a Lego builder more than 35 hours to build the Death Star​?

​(Round to four decimal places as​ needed.)

​c) What is the probability that it takes a Lego builder between 24 and 33 hours to build the Death Star​?

​(Round to four decimal places as​ needed.)

​d) What is the probability that it takes a Lego builder exactly 34 hours to build the Death Star​?

​(Round to four decimal places as​ needed.)

​e) What is the amount of time it takes to build the Death Star such that the amount of time is in the upper 7​% of build​ times?

? hours​ (Round to two decimal​ places.)

​f) What is the amount of time it takes to build the Death Star such that the amount of time is in the lower 19​ of build​ times?

? hours​ (Round to two decimal ​places.)

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	27.13
std deviation   =σ=	5.160

a)

probability =P(X<20)=(Z<(20-27.13)/5.16)=P(Z<-1.38)=0.0838

b)

probability =P(X>35)=P(Z>(35-27.13)/5.16)=P(Z>1.53)=1-P(Z<1.53)=1-0.937=0.0630

c)

probability =P(24<X<33)=P((24-27.13)/5.16)<Z<(33-27.13)/5.16)=P(-0.61<Z<1.14)=0.8729-0.2709=0.6020

d)probability that it takes a Lego builder exactly 34 hours to build the Death Star =0.0000

e)

for 93th percentile critical value of z=		1.48
therefore corresponding value=mean+z*std deviation=			34.77 hours

f)

for 19th percentile critical value of z=		-0.88
therefore corresponding value=mean+z*std deviation=			22.59 hours