Question

Fill in the blanks: The number of hours it takes for a certain part in a manufacturing process to wear out is assumed to be from a population with a normal probability distribution with a mean of 1,350 hours and a standard deviation of 190 hours. If this is true, then approximately 68% of the parts are predicted to wear out between _______ and _______ hours of operation.

Answer 1

what? @nincompoop

Answer 2

@CliffSedge

Answer 3

What's up?

Answer 4

Oh, this is empirical rule: 68% of a normal population will be between ±1σ from the mean.

Answer 5

It's more precisely 68.2689% but it says "approximately."

Answer 6

So the range is 1350 ± 190.

Answer 7

is that the answer?

Answer 8

@CliffSedge

Answer 9

Essentially, you'll have to do the plus/minus part to get the minimum and maximum values.

Answer 10

so i get 1540 and 1160

Answer 11

Yep, that's the approximately 68% range.

Answer 12

okay so how to i got about finding the hours

Answer 13

Those are the hours. 1350hours ±190hours.
Do you know the rest of the empirical rule? The percentages for ±2σ, ±3σ, and ±4σ?

Answer 14

nope we were left to figure this out on our own

Answer 15

Do you have a graphing calculator with statistical functions?

Answer 16

no only a casio

Answer 17

How about a normal distribution table? There are tables and stats calculators available online. Do you have a textbook for the class or are you taking it online?

Answer 18

in class but no book required

Answer 19

Hmm, well at least get access to a normal distribution table. You can solve problems like these by doing a 'reverse lookup' - you find the probability/proportion you want in the body of the table then cross reference it to the associated z-score.

Answer 20

whats my probability/proportion

Answer 21

Try that and verify the following (approximately): ±1σ = 68.27%, ±2σ = 95.45%, ±3σ = 99.73%, and ±4σ = 99.99%.

Answer 22

For this example, the proportion was 68% so you try to find a number in the body of the table that's closest to 0.6800, then read across to the margin to find the z score for that number. You should see that it is 1. That means plus or minus 1 standard deviation away from the mean.

Answer 23

i get 0.1

Answer 24

Er.. well, actually that depends on what kind of table it is. I've seen different kinds. It depends on if it's an interval, or single-sided table. ..

Answer 25

What kind are you using?

Answer 26

standard normal distribution

Answer 27

double sided

Answer 28

Ok, so for example does it say something at the top like "between 0 and z" or "from negative infinity to z?"

Answer 29

from o to z

Answer 30

Ok, those are good for double-sided / interval lookups. So you'll want to find half of 68% or .3400 in the table since half is to the right of 0 and half is to the left of it.

Answer 31

okay i get 1

Answer 32

e.g. using the table at http://www.statsoft.com/textbook/distribution-tables/ I find 0.3389 and 0.3413 which are closest to 0.3400. which means it's between 0.99 and 1.00

Answer 33

Good, so as another example try finding z for 95%

Answer 34

between 2 and 1.9

Answer 35

Excellent! Looks like you got the hang of it.

Answer 36

how do i find the hours though @CliffSedge

Answer 37

@MathLegend any help?

Answer 38

? I'm confused. I gave you the solution and confirmed it twice.

Answer 39

i missed it i dont know what the answer is

Answer 40

its asking for two sets of hours of where the equipment will wear

Answer 41

@CliffSedge

Answer 42

1350hours ±190hours = <1160,1540>