quick binomial distribution question

1 in 5 people is left handed. Find the probability that in a random sample of 10 people, exactly 3 people will be left handed?

is it asking me to do :

so P(X=3) = 10C3.(0.2)^3.(0.8)^7

or is it asking me to do:

E(x) = n x p
Var(x)= n x p x q
standard deviation= √n x p x q

Thankyou :redface:

Reply 1

SlyPie

12

Use the first method.

OP

Thanks!

OP

i have another question but im a lil stuck finding out the values for n and p.

'A crossword puzzle is published each day of the week apart from sunday.
A man can complete on average, 8 out of 10 of the crossword puzzles.

Find the expected mean and standard deviation of the number of completed crosswords in a given week.'

is n=6 and p=8/10?

Reply 4

Mechs

magnum

is n=6 and p=8/10?

yes

E(x) = 6 x 8/10 = 4.8
standard deviation= √6 x 8/10 x 2/10 = 0.39...

OP

fantastic!

OP

'A crossword puzzle is published each day of the week apart from sunday.
A man can complete on average, 8 out of 10 of the crossword puzzles.

'show that the probability that he will complete at least 5 in a given week is 0.655 (3sf)'

how would i do that?

Reply 7

Mechs

magnum

'A crossword puzzle is published each day of the week apart from sunday.
A man can complete on average, 8 out of 10 of the crossword puzzles.

'show that the probability that he will complete at least 5 in a given week is 0.655 (3sf)'

how would i do that?

X~B(6, 8/10)

P(X » 5) = P(X=5) + P(X=6)
............= P(X=5) = 6C5.(8/10)^5.(2/10) = 0.393216
............= P(X=6) = 6C6.(8/10)^6.(2/10)° = 0.262144
............= P(X » 5) = 0.393216 + 0.262144 = 0.655 (3.s.f)

Reply 8

magnum

OP

4

Mechs

X~B(6, 8/10)

P(X » 5) = P(X=5) + P(X=6)
............= P(X=5) = 6C5.(8/10)^5.(2/10) = 0.393216
............= P(X=6) = 6C6.(8/10)^6.(2/10)° = 0.262144

............= P(X » 5) = 0.393216 + 0.262144 = 0.655 (3.s.f)