1. ## Gaussian Distribution

The strength levels of a group of Martians follows Normal distribution with a mean of 75kgf and a std. dev. of 5kgf.

(a) How many Martians do you expect to meet before you find one with a strength level greater than 72 kgf?

(b) In a group of 5 Martians, what is the probability that exactly 4 Martians have strength levels greater than 72 kgf?

(c) 4 Martians are trying to open a huge stone door which will open only if all of their individual strength levels are greater than 72 kgf. What is the probability that they will open the door?

EDIT: Never mind I figured out (a) and (c). Still need help on (b), though. Thanks. I'll probably kick myself for not seeing it, but oh well.

2. Originally Posted by thefirsthokage
The strength levels of a group of Martians follows Normal distribution with a mean of 75kgf and a std. dev. of 5kgf.

(a) How many Martians do you expect to meet before you find one with a strength level greater than 72 kgf?

(b) In a group of 5 Martians, what is the probability that exactly 4 Martians have strength levels greater than 72 kgf?

(c) 4 Martians are trying to open a huge stone door which will open only if all of their individual strength levels are greater than 72 kgf. What is the probability that they will open the door?

EDIT: Never mind I figured out (a) and (c). Still need help on (b), though. Thanks. I'll probably kick myself for not seeing it, but oh well.
Calculate the probability p(72) that a martian has strength > 72 kgf. Then
the number with strength >72 kgf in a sample of 5 has a binomial distribution
B(p(72), 5). So prob of 4 having strength >72 kgf is b(4, p(72), 5).

RonL