Question

A brewery's filling machine is adjusted to fill bottles with a mean of 32.1 oz. of ale and a variance of 0.006. Periodically, a bottle is checked and the amount of ale noted.
(a) Assuming the amount of fill is normally distributed, what is the probability that the next randomly checked bottle contains more than 32.25 oz? (Give your answer correct to four decimal places.)


(b) Let's say you buy 94 bottles of this ale for a party. How many bottles would you expect to find containing more than 32.25 oz. of ale? (Round your answer up to the nearest whole number.)
bottles

Answer 1

@amistre64 help here

Answer 2

... so i get the novels lol

Answer 3

haha sorry i can not figure out how to do this at all. :(

Answer 4

once the words are sorted thru, the rest is formulaic i believe

Answer 5

mean of 32.1
variance of 0.006

prob more than 32.25

Answer 6

what methods are you able to use? ti83 calculator, or ztable?

Answer 7

i use the ti-84 calculator.

Answer 8

then this is going to be simple

Answer 9

haha i cant figure out where to type it all in at. i keep getting zero as the answer.

Answer 10

2nd, VARS should get you to the distribution functions

pick normalCDF as your function

Answer 11

okay

Answer 12

you are going to enter 4 parameters

(low,high,mean,sd)

since we want greater then 32.25; our low is going to be 32.23

our high has no stopping value so we need to input an arbitrary large number; 9999 is the usual

the means is given

and the sd is the sqrt variance

Answer 13

is it really that simple?! lol. thanks so much :)

Answer 14

your welcome, and yes; its that simple ... at least for a)

Answer 15

b is easy once you have the prob from a

what is 94*prob from a

Answer 16

that wasnt right? and then wen i tried to do it again it gave me zero as the asnwer again?

Answer 17

what value do you have as the sd?

Answer 18

o wait i was using variance, how do i do sd?

Answer 19

wait got it lol.

Answer 20

cool

Answer 21

still was wrong wen i entered it. that was my last chance too. so how do u do b?

Answer 22

b is using the probability from a, and multiplying it by 94

Answer 23

you have to round it to 4 decies; make sure your rounding is good.

is the program expecting you to use a ztable perhaps?

Answer 24

o okay. well if i didnt find the right probability what should i do?

Answer 25

yea i think my rounding was off for the sd

Answer 26

if it gives you a new problem, lets work with those values

also, if your using a mathlab type program, there should be a "solve similar" option to make sure we are conforming to its programming

Answer 27

if it gave you the correct answer it wants for a, then use that to multiply by 94 (we want the percentage of bottles out of 94)

Answer 28

it doensnt give the correct answer. i tried to do it again and multiply it by 94 but that was wrong for part b. it doesnt give u more practice problems tho.

Answer 29

how do u use a ztable? c if u tried it and c what u get.

Answer 30

z tables are less accurate than a calculator, so if its expecting a ztable result it might consider the calc answer as off.

Answer 31

do you have a ztable handy?

Answer 32

o but no i dont is there one online?

Answer 33

there are lots online yes

http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

heres one that pops up form the google

Answer 34

we need to determine the zvalue of 32.25; to do that, we can use the formula

z = (x-mean)/sd ; where sd = sqrt(var)

z = (32.25-32.1)/sqrt(.006)

Answer 35

i got 1.9365?

Answer 36

lets say that is: z = 1.94

split that up into 1.9 and .04

we use the table by finding 1.9 on the left side; and .04 on the top and seeing where they meet up at in the feild

Answer 37

i got .9738?

Answer 38

yes

now we have to know that the table we are using is giving us the value of all the stuff that is LESS THAN 32.25

the whole thing is equal to 1, so we need to find the rest of it

1 - .9738 is going to be the stuff the is GREATER THAN 32.25

Answer 39

so its .0262?

Answer 40

yes, and i hope you see why we had to flip it.

1.0000
- .9738
---------
.0262 should be it; is that close to what you had with the calculator?

Answer 41

no i was getting .0466 lol so now i just multiply that by 94?

Answer 42

the probability is also a percentage; it tells us that: 2.62 % of the stuff falls within our details

Answer 43

if we have a total of 94, we should expect 2.62% of them to fall within our expectations

Answer 44

so to get B would u multiply by .0262 * 94?

Answer 45

your in stats, you should know how to find a percentage of a total by now :)

but yes

Answer 46

haha yes i got that. thanks so much :)

Answer 47

does it like our answer tho?

Answer 48

nope still wrong and that was my last chance. no biggie thanks tho.

Answer 49

did you rnd your answer up to the nearest while number?

Answer 50

*whole number

Answer 51

yea it should have been 2 but it said it was wroing lol.

Answer 52

94*.0262 = 2.4628; rnds up to 3

Answer 53

well dang it thats why. i thought u would take the .4 and that doesnt round up.

Answer 54

think of it this way

you have 2 wholes; and part of another one

we dont want a value that is less than what is expected, and we dont get partial bottles

we would need to move UP to 3 to cover the extra more than 2

Answer 55

okay yea true dang it. o well.

Answer 56

:) good luck

Answer 57

thanks so much.