How to do part b)? Question 4: Score 2/4 Extruded plastic rods are automatically

Question

How to do part b)?

Question 4: Score 2/4 Extruded plastic rods are automatically cut into nominal lengths of 12.0 cm. Actual lengths are normally distributed about a mean of 12.0 cm and their standard deviation is 0.4 cm. a) What proportion of the rods have lengths that are outside the tolerance limits of 11.2 to 12.8 cm? Give your answer to three decimal places. Your response 0.0455 Correct response 0.046±0.002 Grade: 1/1.0 b) To what value does the standard deviation (in cm) need to be reduced if 98.1% of the rods must be within tolerance? Answer to two decimal places. Your response Correct response 0.34+0.01 Grade: 0/1.0

Explanation / Answer

Ans:

b)

Area within tolerance limits=0.981

Area outside tolerance limits=alpha=0.019

alpha/2=0.019/2=0.0095

z=normsinv(0.0095)=-2.35 or z=normsinv(1-0.0095)=2.35

Now,

z=2.35=(12.8-12)/sd

sd=0.8/2.35=0.34

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