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.

Quote:

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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.

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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