Problem 5 (Statistical Tolerancing). (USE R) You go to a hardware store to buy a

Question

Problem 5 (Statistical Tolerancing). (USE R) You go to a hardware store to buy a door for the front entrance to your home. The frame for the door is 202 cm in height. The dimensions of doors vary due to natural manufacturing variability. From historical data we know that X, the height of doors is normally distributed with a mean 201 cm and a standard deviation of 1 cm. We want a door that will fit inside the frame. We also want a door that won't leave to much room between the frame and the door. So we want a door whose height is between 200 and 202 cm. (a) What is the probability that the chosen door will satisfy the height re- quirement? (b) What is the height such that 80% of the doors are at or below that height?

Explanation / Answer

Sol:

mean=201

sd=1

P(200<X<202)

Z=X-MEAN/SD

P(200-201/1<Z<202-201/1)

=P(-1<Z<1)

=P(Z<1)-P(Z<-1)

rcode is:

Result<- pnorm(1)-pnorm(1, lower.tail=FALSE)
Result

=0.6826895

ANSWER:0.6826895

SOlutionb:

Rocde is

pnorm(0.84)

that is P(Z<0.84)=0.7995

Area is 80% for Z<0.84

we have

z=x-mean/sd

0.84=x-201/1

x=201+0.84

x=201.84

ANSWER:
the height is 201.84 such that 80% of the doors are at or below that height

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