finding probability

[summertigger]

According to the Bureau of Navel Standards, 75 percent of all people are "inners," (that is their belly buttons poke inward); everyone else is an "outer." Let the random variable x be the number of outers among 7 randomly selected persons.

Find the mean and variance of x
Find the probability that exactly 2 of 7 persons are outers.
Find the probability that no more than 6 of 7 are outers.
Find the probability that none of the 7 is an outer.

Im not sure where to even begin with this problem! Help is greatly appreciated!

[JohnM]

We have examples of this type of problem here:

http://www.talkstats.com/examples/146-binomial-probabilities.html

[summertigger]

Find the Probability that exactly 2 of the 7 persons are outers

Let me know if Im on the right track...
N=7
r=2
p=.25
q=.75

7!/2!5!*(.25)2(.75)5
=5040/240
=21(.06)(.24)
=.30 that they will be an outie

[JohnM]

The actual answer is 0.311 - you may have some rounding error, but you did everything correctly - good job!

[summertigger]

Find the probability that no more than 6 of the 7 are outers

7!/6!1!*(.25)2(.75)5
=5040/720
=7(.06)(.24)
=.10

[JohnM]

I explained this one in the private message.

[feldner]

I am currently working with this same problem and would appreciate some guidance. (I checked the link provided)

Is this the correct variance and mean?

7(.25)=1.75 mean
7(.25)(1.75)=1.3125 variance

I think I have the correct answer for the probability that 2 or the 7 are outers. (.311463)


The probability the none of the 7 is an outer?
n=7, p=.25, x=0

7!1/7-0!0!(.25)0exponent(.75)7exponent

1(1)(.75)7exponent=.133484 probability that none of 7 is outer.


Find the probability that no more than 6 of the 7 are outers?

Okay now this one I'm lost on I tried to work it and came up with the answer
.998718, but don't think this is correct. I see where it was worked previously with an answer of .10, is that the correct answer and the correct way to work this section of the problem?

Thank you so much for any help. Jill

[JohnM]

The probability of no more than 6 outers is the same as:

1 - P(7 outers)

= 1 - (.25)^7

= 1 - .000061

= .999939