Question

Can I get some help with this?
Use normal approximation to estimate the probability of passing a true/false test of 50 questions if the minimum passing grade is 90% and all responses are random guesses.

Answer 1

approximately 0 hahaha

Answer 2

Well, have at it! Show your work.

Answer 3

have you covered binomial probability?

Answer 4

a formula you can use to solve this problem is C(n,r)*p^r*(1-p)^(n-r)

Answer 5

though that formula is more than you need, as it reduces down to a pretty simple answer because p=1-p=.5

Answer 6

so n=50 and p=0.5
np=25
rootnpq= root12.5
p(x>=45) (44.5 after continuity correction)
calculating z score so x-mean/sd
44.5-25/root 12.5 = 5.5
Posting this in case anyone wants to see the process I tried. I'll try out the binomial formula now and see how it goes

Answer 7

I believe I cannot help you here. I can offer the answer but i do not know how to use normal approximation.

Answer 8

what zscore did you get though?

Answer 9

5.5 was my zscore. Which sounds kinda off to me

Answer 10

here is the exact probability if you are curious
http://www.wolframalpha.com/input/?i=C%2850%2C45%29*%28.5%29%5E50

Answer 11

I do not know how close a normal approximation would be, but I think within an order of magnitude is reasonable. I looked up your 5.5 sigma z score and it does seem off by 3 orders of magnitude.

Answer 12

well, after the z score, they want me to use the table to find the probability as well

Answer 13

It's an online assignment, I don't think the wolfram answer will fit

Answer 14

oh, I was giving that as a guideline... that is the actual answer if you use binomial probaiblity theorem, but you are using some kind of approximation so you should get a close but not identical answer

Answer 15

ah, well thank you anyways. They still want a z-score though

Answer 16

question: why subtract for continuity correction?

Answer 17

They requested me to in the first part of the question while looking for z score
a) z-value (Use continuity correction) =

Answer 18

I subtracted rather than added since I assumed >= rather than just >.
Also tried out adding, but the answer was still roughly the same.

Answer 19

well, if it makes you feel any better, I did some quick googling and came up with the same result as you did, although I do not believe I understand when to add or subtract the .5 value for continuity correction... I would go witht he answer that you have right now

Answer 20

just make sure the addition or subtraction for continuity correction is right, because I think that's what'll get you here

Answer 21

I submitted my answer and it's incorrect. I have two more tries.

Answer 22

well, I would suggest adding for continuity correction

Answer 23

I dont' want to waste your tries though.

Answer 24

maybe @jim_thompson5910 could help.. I need to head off to bed. good luck!

Answer 25

Hm, I got 5.8 z score and it's still wrong. Thanks, have a good night!

Answer 26

I'm getting z = 5.5154328 basically what you got before.

P(X >= 45)

turns into

P(Z > 5.52)

most tables don't go as high as z = 5.52 on the table. The highest I've seen is about z = 3 or so. The probability is so small that it is pretty much 0.

Answer 27

not sure why I got a wrong answer with 5.5 but 0 seems to go in just fine. thank you though!

Answer 28

oh pellet, I tried again with 5.52...it's a rounding error. 5.52 is right

Answer 29

you're welcome