Question

Please help me with this:

Approximately 9% of U.S. children have asthma. Consider an elementary school with 500 children.

1. What is the probability that AT LEAST 45 children have asthma?
2. What is the probability that AT MOST 39 children have asthma?
3. What is the probability that AT MOST 51 children have asthma?

Answer 1

Interesting problem -- it looks like you use binomial distribution, but I'm not 100% sure on that.

Answer 2

Ok. Thanks for trying. Are you familiar with margin of error?

Answer 3

Nope. I haven't learned that much in this field. Sorry! ):

Answer 4

Oh, Okay. Well thank you for trying. (:

Answer 5

Maybe @FoolForMath would have a better idea about this... D:

Answer 6

Poisson's formula?

Answer 7

It deals with P= probability & N=trials

Answer 8

Use the binomial probability distribution formula


P(X = x) = (n C x)*((p)^x)*(1-p)^(n-x)


This formula works for small values of x when it comes to computing cdf values (since you're adding individual values to compute the cdf)


However, larger x values make things tedious. So it's better to use a calculator.


One can be found here:

http://stattrek.com/online-calculator/binomial.aspx

Answer 9

How would i plug in my numbers?

Answer 10

Well since x = 45, you need to add up 45 different values to find the cdf...which is way too tedious.


So it's better to use the calculator. Follow that link and type in 0.09 for the probability (since 9% have it), 500 for the number of trials, and 45 for the value of x

When you hit "calculate", it'll give you every bit of information concerning 45 successes


The piece of info you want is P(X >= 45) which will be the last box


This is all of course for #1. You'd do the same (but with different numbers) for #2 and #3

Answer 11

Ok, so it gives me like $ answers, which one do i use?

Answer 12

for #1, you want the last answer because you want to find P(X >= 45) (since you want AT LEAST 45)

Answer 13

for #2 and #3, you want the second box answer (use different numbers of course)

Answer 14

Oh. Ok, thank you SOO much. (: So would 57% be 0.57 or 0.057?

Answer 15

which problem are you referring to, #1, #2, or #3?

Answer 16

57% is 0.57 in decimal form

Answer 17

Thank you. Its on a complete different problem. just making sure of that.

Answer 18

oh ok, just making sure

Answer 19

So for problem #2, the seconf answer is 0.154 The only multiple choice answers i have are
0.16 0.34 0.84 1

Answer 20

hmm that's interesting...maybe there's a typo somewhere or a roundoff error. The closest thing is 0.16, so that's my best guess.

Answer 21

The Same thing for my Other problems.

Answer 22

for #3 as well? what are your choices there?

Answer 23

0.135
0.16
0.34
0.84

Answer 24

I will skip that. Do you know anything about Margin of Error?

Answer 25

it looks like the answer to #3 is 0.84

Answer 26

yes, what do you want to know about it

Answer 27

My paper says: Find the margin of error for a survey that has the given sample size. Round your answer to the nearest tenth of a percent:
1. 225
2. 100
3. 625
4. 3600
5. 4200
6. 776
7. 390
8. 8000

& my answer box has answers like: + or - 1.1% , + or - 3.5%

How do i do this?

Answer 28

Are you given a standard deviation?

Answer 29

No.

Answer 30

It says something about use this formula: + or - 1/squareroot of N

Answer 31

so then the margin of error for #1 is

ME = +- 1/sqrt(N)

ME = +- 1/sqrt(225)

ME = +- 1/15

ME = +- 0.0667

ME = +- 6.67%

ME stands for the Margin of Error and +- is shorthand for + or -


You'd do the same for the rest.

Answer 32

Ok so, number 2 would be: 0.1 so, +-1.1% ?

Answer 33

yes you nailed it

Answer 34

(: Thank you.
can you help me with the last one, 8000. i got the answer 0.0111803399

Answer 35

You got that one as well, so the margin of error is +-1.1%

Answer 36

Thank youuu (:

Answer 37

oh wait, I'm not thinking, the margin of error for #2 is +-10%, not +-1.1%...sorry about that

Answer 38

oh ok. so # 4 3600 would be: +-1.7%

Answer 39

yes since 1/sqrt(3600) = 0.017 which converts to 1.7%

Answer 40

& number 5 would be 0.015430335 so, +-1.5%

Answer 41

yes it is, nice work

Answer 42

Ok, im stuck on this one. 1/SR390 = 0.0506369684

Answer 43

Good, so the margin of error is +-5.1%

Answer 44

Your a life saver. Can you help me with one more thing?

Answer 45

sure thing

Answer 46

In a survey of 802 people, 16% said they use the internet or email more than 10 hours per week.
1. what is the margin of error for the survey?
2. Give an interval that is likely to contain the exact percent of all people who use the internet or email more than 10 hours a week.

Answer 47

# 1

Margin of error

ME = +-1/sqrt(N) x 100

ME = +-1/sqrt(802) x 100

ME = +-1/28.3196 x 100

ME = +-0.035 x 100

ME = +-3.5%


So the margin of error is +-3.5%

----------------------------------------------------------

# 2

The margin of error is 3.5%

So this means that our estimate 16% may be 3.5% too high or 3.5% too low.

If it's 3.5% too high, then the lower bound of the interval is 16 - 3.5 = 12.5%

If it's 3.5% too low, then the upper bound of the interval is 16+3.5 = 19.5%


So the interval likely to contain the exact percent is (12.5%, 19.5%)


You're most likely going to express the percentages in decimal form, so the interval is (0.125, 0.195)

Answer 48

Thank you so much. (: This is pretty easy now. Can i ask one more favor?

Answer 49

can you help me with the opposite of what we did earlier?

Answer 50

which one do you want me to do as an example?

Answer 51

number 54 & then 59 since there different, please

Answer 52

I'm going to express everything in decimal form (so something like 5.7% is 0.057). Also, I'm going to ignore the +- for now.


# 54


ME = 1/sqrt(N)

0.07 = 1/sqrt(N)

0.07*sqrt(N) = 1

sqrt(N) = 1/0.07

sqrt(N) = 14.2857

N = (14.2857)^2

N = 204.081

N = 204


So a sample size of 204 gives you a margin of error of +-7%

=============================================

# 59


ME = 1/sqrt(N)

0.022 = 1/sqrt(N)

0.022*sqrt(N) = 1

sqrt(N) = 1/0.022

sqrt(N) = 45.4545

N = (45.4545)^2

N = 2066.11157

N = 2066


So a sample size of 2066 gives you a margin of error of +-2.2%

Answer 53

For number 55 somehow i got the answer 16.665?

Answer 54

i did it again and got 277

Answer 55

good, your second answer of 277 is correct

Answer 56

its not any of my answers tho.

Answer 57

i have 278 as an answer choice

Answer 58

that's close enough, 278 gives a margin of error of 5.99% which is very close to 6%

Answer 59

Okay, Thank you so much. (:

Answer 60

you're welcome