probability

1)
a man tosses a peny 8 times. for each head he moves 1 metre west and for each tail he moves 1m east. find the probability :

a) that he will end up at his starting position
b) he will end up more than 3m from his starting point

2)
a manufacturer produces airmail envelopes whose weight is normaly distributed with mean =1.950grams and s.d = 0.025 grams. the envelopes are sold in lots of 1000. how many envelopes in a lot will be heavier than 2grams

Reply 1

Jonny W

(1)
His final position is x - (8 - x) = 2x - 8 units west, where x is the number of heads.

(a)
P(exactly 4 heads) = (8!/(4!4!))(1/2)^8 = 35/128

(b)
P(0, 1, 2, 6, 7 or 8 heads)
= 2*P(0, 1 or 2 heads)
= 2*(1/2)^8 (1 + 8 + 8!/(2!6!))
= 37/128

(2)
P(a randomly selected envelope is heavier than 2 grams)
= 1 - Phi((2 - 1.95)/0.025)
= 1 - Phi(2)
= 0.02275

In a lot of 1000 envelopes there will be on average 1000*0.02275 = 22.75 envelopes that are heavier than 2 grams.

Reply 2

popat

i dnt get y its 2x-8 for 1a

Reply 3

Jonny W

popat

i dnt get y its 2x-8 for 1a

If there are x heads then there are (8 - x) tails.

Each head moves the man one metre west.

Each tail moves the man one metre east.

The man's final position is the following distance west of his initial position:

(number of heads) - (number of tails)
= x - (8 - x)
= 2x - 8.