Question

Fan and Medal!

Market research has shown that 60% of the customers at an electronics store opt to pay for their purchases by installments.

There are 24 customers at the electronics store on a particular morning. Find the probability that the 8th customer to the store is the 4th customer who opts to pay for this purchase by installments, and there are less than 10 customers opting to pay by installments.

Answer 1

The binomial distribution can be used to solve the first part.
\[\large P(3\ from\ first\ 7\ use\ instmnt)=C(7, 3) \times0.6^{3}\times0.4^{4}\ .....(1)\]
The probability that the 4th customer pays by installments is 0.6.
Therefore to find the required probability, multiply the result of (1) by 0.6.

Answer 2

X~B(7,0.6)
P(x=3).0.6

Answer 3

what about less than 10 opting for installments ? @kropot72

Answer 4

@ganeshie8 @thomaster hlp pls :(

Answer 5

I recommend using the normal approximation to the binomial distribution for the second part.
The mean is np and the variance is npq, giving:
\[\large mean=np=24\times0.6=14.4\]
\[standard\ deviation=\sqrt{24\times0.6\times0.4}=2.4\]
You will need to use the 'continuity correction', the reason being we are using a continuous distribution to approximate a discrete distribution.

Answer 6

im suppose to solve it using binomial distribution only

Answer 7

nvm then.. thanks anyway :)

Answer 8

In that case you need to calculate the individual binomial probabilities for 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 out of 24 opting for installments. Then sum these 10 values of probability.

Answer 9

\[\large P(0)=0.4^{24}\]
\[\large P(1)=24\times0.6\times0.4^{23}\]
and so on.

Answer 10

@HatcrewS Can you handle that?

Answer 11

nope.. i dont know what you doing.. :(