Question

@Blank  @jim_thompson5910

Answer 1

@Blank 

Answer 2

What do u need help with? :)

Answer 3

In a random sample of 700 refreshment-dispensing machines, it is found that an average of 8.1 ounces is dispensed with a natural deviation of 0.75 ounce.

28. Find the standard error of the mean. Round your answer to the ten-thousandths place.

Answer 4

29. Find the probability that the mean of the population will be less than 0.085 ounce from the mean of the sample. Round your answer to the tenths place.

Answer 5

No. just an answer.

Answer 6

30. Find the probability that the true mean is between 8.157 and 8.185. Round your answer to the tenths place.

Answer 7

And thats it

Answer 8

Ok

Answer 9

The answer to number 29 is a percent

Answer 10

thanks. and 30?

Answer 11

it says round the answer to the tenths place @jim_thompson5910 can you help?

Answer 12

@jim_thompson5910

Answer 13

which one?

Answer 14

can you help on #30?

Answer 15

convert those raw scores to z scores

use: z = (x-mu)/sigma

Answer 16

tell me what z scores you get

Answer 17

turn 8.157 and 8.185 into z scores right?

Answer 18

yeah

Answer 19

sigma=700 right?

Answer 20

n = 700 (sample size)

Answer 21

sigma = 0.75

Answer 22

z=0.076 and 0.113

Answer 23

correct

Answer 24

now use this table

http://www.math.upenn.edu/~chhays/zscoretable.pdf

Answer 25

to find the area to the left of z = 0.08 (I rounded z = 0.076 to 2 decimal places)

Answer 26

ok

Answer 27

now what? @jim_thompson5910

Answer 28

what area did you get?

Answer 29

Wait Im confused

Answer 30

about what

Answer 31

From where you said use the table, what did you want me to do?

Answer 32

the table lets you find the area under the curve to the left of a given z score

Answer 33

do you remember how to read the table?

Answer 34

ok but what score do i find?

Answer 35

z = 0.08

locate the 0.0 row, then find the 0.08 column

the value in that row/column combo is the area to the left of z = 0.08

Answer 36

look on page 2

Answer 37

0.5319

Answer 38

what is the area to the left of z = 0.11

Answer 39

I'm getting z = 0.11 from rounding z = 0.113

Answer 40

what area? on the graph?

Answer 41

the table provides the value

Answer 42

this whole table tells you the area to the left of a given z score

Answer 43

0.0?

Answer 44

0.11 starts with 0.1

look in the 0.1 row

Answer 45

ok then what

Answer 46

look in the column that finishes up z = 0.11

Answer 47

0.1 is already taken care of, so the missing bit is that last 1

that's what the column 0.01 means

ie

0.11 = 0.1 + 0.01

Answer 48

ok

Answer 49

0.5438

Answer 50

now subtract the two areas

Answer 51

0.5319-0.5438=-0.0119
OR 0.5438-0.5319=0.0119

Answer 52

the area will be positive, so 0.5438-0.5319=0.0119

Answer 53

the area between z = 0.08 and z = 0.11 is roughly 0.0119

Answer 54

that means the area between x = 8.157 and x = 8.185 is also roughly 0.0119

Answer 55

Ok now what

Answer 56

the area under the curve is the same as finding the probability (think of randomly throwing a dart onto the right area)

Answer 57

Find the probability that the true mean is between 8.157 and 8.185. Round your answer to the tenths place.

0.0119 rounds to 0.01

that's roughly a 1% chance

Answer 58

And thats the answer? 1%?

Answer 59

oh wait, not 0.01...it should be 0.0

hmm seems odd

Answer 60

let me recheck

Answer 61

ok

Answer 62

oh I used the wrong standard error

Answer 63

z = (x - mu)/(sigma/sqrt(n))

z = (8.157 - 8.1)/(0.75/sqrt(700))

z = 2.01

Answer 64

what's the area to the left of z = 2.01 ?

Answer 65

there is no colomn for 2.01

Answer 66

combine row 2.0 with column 0.01

notice how they add to 2.01

2.0 + 0.01 = 2.01

Answer 67

oh

Answer 68

0.9778

Answer 69

each row/column combo gives you pretty much every z value from z = -3.49 to z = 3.49

Answer 70

going in increments of 0.01

Answer 71

correct

Answer 72

z = (x - mu)/(sigma/sqrt(n))

z = (8.185 - 8.1)/(0.75/sqrt(700))

z = 2.9985

z = 3.00

Answer 73

find the area to the left of z = 3.00

Answer 74

0.9987

Answer 75

subtract the two

Answer 76

0.0209

Answer 77

That still gives 0.0, how annoying

honestly, it's better to write it to at least 2 decimal places

Answer 78

ok i will do that

Answer 79

Thank you for all of your help. I greatly appreciate it! :)

Answer 80

you're welcome