Thanks to John M & more questions

[orangeb]

Thanks to John M for all of his help! I have several more questions that I got wrong answers on and would like to know the correct answers if anyone would like to tackle them.

Question #1 I need to find Carl's percentile rank among all of these people.

Jill 199 Hank 255
Ebb 227 Ian 255
Al 243 Gert 261
Bess 255 Flo 279
Carl 255 Delia 312

I had the answer as his rank being the 40th percentile and it was marked wrong.


Question #2 The Drama club (12 guys, 9 girls) will perform a tribute to the Waltons. Part A:In how many different ways can the roles of John Boy, Jason and Jim-Bob be cast from among the 12 guys?
Part B: In how many different ways can the 3 member Publicity Committee be formed among the 9 girls?

I had the answer to Part A as 220 ways and Part B as 84 ways. Can anyone show me the correct answers and the steps to get it?


Question #3 The IRS says it will audit about 20% of all tax returns next year. What are the odds in favor of your being audited?

[JohnM]

(1)
Compute the mean and standard deviation
Compute the z score for Carl's score
z = (255 - mean)/std dev
find the proportion of the area under the normal curve below z

(2)
A: 12C3 = 12! / ( 3! (12-3)! )
B: 9C3 = 9! / ( 3! (9-3)! )

(3)
odds in favor = prob(happens) / prob(doesn't happen)

[orangeb]

[QUOTE=JohnM](1)
Compute the mean and standard deviation
Compute the z score for Carl's score
z = (255 - mean)/std dev
find the proportion of the area under the normal curve below z


I came up with the answer of .0319943. Is this correct or am I still off?

[orangeb]

[QUOTE=JohnM
Question(2)
A: 12C3 = 12! / ( 3! (12-3)! )
B: 9C3 = 9! / ( 3! (9-3)! )

I am still coming up with 220 for A and 84 ways for B. Are these correct?

[JohnM]

Actually, after looking again, A should be:

12P3 (permutations, rather than combinations) = 1320

For B, 84 is correct.

[jerryb]

to add onto johns answer,

use permutations anytime the order of selection matters. such as first, second or third prize. in this case order does matter since playing jim-bob would likely be percieved as less desireable than playing jon-boy.

cheers
jerry

[feldner]

[QUOTE=orangeb]

(1)
Compute the mean and standard deviation
Compute the z score for Carl's score
z = (255 - mean)/std dev
find the proportion of the area under the normal curve below z


I came up with the answer of .0319943. Is this correct or am I still off?

Is the answer .0319943 correct? Apparently, I am lost, this is how I figured the above percentile:
x=[(B+1/2E)/ N] x 100
[3+1/2(4)]/10 x 100
3+2/10 x 100
5/10x100 = 500/10 = 50 percentile rank??? Is this incorrect and the above answer correct??

[JohnM]

Your method is just another correct way to determine percentile rank....your answer is fine. As long as you get something in the ball-park of the 50th percentile.

[feldner]

You are a genius!! Thank you!!