Question

suppose the diameter of an electric cable is normally sistributed with mean 0.8 and standard deviation .02. a cable is considered defective if the diameter differs from the mean by more than .025. you will randomly select electric cables until you find a nondefective cable. what is the probability that you find that non defective cable on the sixth observation?

Answer 1

Do you know how to find the z-scores for 8.025 and 7.975, these being the limits for a non-defective cable?

Answer 2

kinda need help on that too

Answer 3

\[z _{1}=\frac{X-\mu}{\sigma}=\frac{8.025-8.000}{0.02}=you\ can\ calculate\]

Answer 4

now i get it... thank you so much.. took me like 2 hours to figure that out. :)

Answer 5

Have you calculated the value of z1 yet?

Answer 6

its 1.25

Answer 7

Correct! Now for the z-score for 7.975:
\[z _{2}=\frac{7.975-8.000}{0.02}=you\ can\ calculate\]

Answer 8

-1.25

Answer 9

Good work. Correct again!
The next step is to find the probability that a randomly sampled cable has a diameter between 7.975 and 8.025. To do this we can use a standard normal distribution table and find the cumulative probabilities for z-scores of 1.25 and -1.25. Then the smaller probability is subtracted from the larger.
You can use the standard normal distribution table here if you like:
http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

Answer 10

2.50?

Answer 11

Not really. You don't subtract the z-scores, rather you subtract the probability values which apply to the z-scores. These probability value are found from the table that I posted a link for. Have you looked at the table and found the probability for a z-score of -1.25?

Answer 12

.1056?

Answer 13

Very good work! Now can you find the probability for a z-score of 1.25?

Answer 14

.8644

Answer 15

The probability for a z-score of 1.25 is 0.8944 according to my reading of the table.

Answer 16

oops you are correct. it was my mistake lol

Answer 17

one question how come its 8.0 instead of 0.8?

Answer 18

Therefore the probability that a randomly sampled cable has a diameter between 7.975 and 8.025 is given by:
\[P(z _{1})-P(z _{2})=0.8944-0.1056=0.7888\]
The probability that a randomly sampled cable does not have a diameter between 7.975 and 8.025 is given by:
1.0000 - 0.7888 = 0.2112
To find the required probability we need to find the probability that the 5 first samples result in a non-conforming cable each time and the sixth sample is a conforming cable. This is given by:
\[P(non-defective\ is\ sixth\ observatio)=(0.2112)^{5}\times0.7888=you\ can\ calculate\]

Answer 19

0.00033?

Answer 20

Good work again! That is the correct answer :)

Answer 21

one question: why we use mean 8 instead of 0.8?

Answer 22

Very sorry! My bad :(
I incorrectly read the question and took the mean diameter to be 8 instead of the stated 0.8. I will recalculate. Please wait.

Answer 23

okay thank you :)

Answer 24

When the correct value of mean is used, the z-scores come to the same values as with a mean of 8. Therefore all the calculations following the z-scores are still correct:)

Answer 25

oh cool. thank you for helping me :D

Answer 26

\[z _{1}=\frac{0.825-0.8}{0.02}=1.25\]
\[z _{2}=\frac{0.775-0.8}{0.02}=-1.25\]

Answer 27

You're welcome :)

Answer 28

lol very close call.. same answer. once again thank you :)

Answer 29

np :)