Question

Extruded plastic rods are automatically cut to nominal lengths of 6 inches. Actual lengths are normally distributed with a mean of mean of 6 inches and a standard deviation of 0.06 inches.

a. Tolerance limits for these rods are 5.9 to 6.1 inches, or in other words, within plus or minus 0.1 of the mean. What proportion of the rods is within tolerance limits?

Answer 1

@Euler271 or @satellite73 Do you think you could give me a hand? :/ Would be very appreciated!

Answer 2

@jim_thompson5910 @Directrix @UnkleRhaukus are you guys any good with stats? I sure could use some help!

Answer 3

@Loser66 @dan815
Sorry im grasping for straws here. :S

Answer 4

are you allowed to use a calculator?

Answer 5

Sure am.

Answer 6

ok I recommend you use wolfram alpha, let me pull that website up

one sec

Answer 7

if you type in "normalcdf" without quotes into wolfram alpha, you'll get this page

http://www.wolframalpha.com/input/?i=normalcdf

Answer 8

then you click on the "use mean" and "use standard deviation" links

and you also click on the " left endpoint and right endpoint " link as well

Answer 9

that will set you up to use the calculator and you type in the following


mean: 6
standard deviation: 0.06
left endpoint: 5.9
right endpoint: 6.1


and you calculate it out

Answer 10

So P=(-1.66=>z<=1.66)

Answer 11

one sec

Answer 12

you should have gotten this


http://www.wolframalpha.com/input/?i=normalcdf&a=*C.normalcdf-_*Formula.dflt-&f2=6&f=NormalProbabilities.mu_6&f3=0.06&f=NormalProbabilities.sigma_0.06&f4=5.9&f=NormalProbabilities.l_5.9&f5=6.1&f=NormalProbabilities.r_6.1&a=*FVarOpt.1-_***NormalProbabilities.l-.*NormalProbabilities.r--.***NormalProbabilities.z--.**NormalProbabilities.pr---.**NormalProbabilities.mu-.*NormalProbabilities.sigma---

Answer 13

So its 1.66 standard deviation to the right of the mean and 1.66 standard deviation to the left of the mean.

Answer 14

nvm I got it, sorry for the inconvenience.

Answer 15

no you look at the portion where it says "confidence level" and that's where your answer is

so the answer is 0.9044

Answer 16

but it sounds like you figured it out?

Answer 17

Yeah in stats right now we are covering normal distribution.
In this case we have P(5.9<x<6.1)

or P(-1.66<z<1.66) z=(value-mean)/standard deviation

same as P(z<-1.66) - (z< 1.66) and then we are suppose to look up the value for z in a table for -.1.66 and 1.66 and subtract and that would be the answer.

Answer 18

https://statistics.laerd.com/statistical-guides/normal-distribution-calculations.php#betweentitle

under P(–a < Z < b) if you're interested.

Answer 19

ok one sec

Answer 20

sorry got distracted for a sec, but yeah it looks like you figured it out

you convert to standard normal variables

then you use the table to compute P(Z < -1.66) and P(Z < 1.66)

then subtract those two values to get your answer

Answer 21

No problem. Thanks for the nudge in the right direction!

Answer 22

you're welcome