Question

The probability a pupil takes a bus to school is 0.3. If a sample of 10 pupils are chosen at random. Using binomial distribution. Find the probability that
a) exactly four pupils travel by bus.
b) more than six pupils travel by bus.

Answer 1

P(4) = C(10,4) .3^4 .7^6

C(10,4) = 10!/[4! 6!]

= 10*9*8*7/[4*3*2] = 30*7 = 210

so
P(4) = 210 * .3^4*.7^6

= 0.02

for the second part do that for
7 8 9 and 10 students and add results. Do not spend more that a week at it. If you get frustrated you can approximate a binomial distribution by a normal with
mean = n p = 10*.3 = 3
sigma^2 = np(1-p) = 10*.3*.7
= .21
so
sigma = sqrt .21 = .458
then use
http://davidmlane.com/hyperstat/z_table.html