(Business Mathematics &Statistics)?

Question

If a coin is tossed 4 times and the probability of success in each trial is the probability of getting a head (p=0.5). Then find the smallest value for which the cumulative binomial distribution is greater than 0.75. (Use “CRITBINOM” function)

Answer 1

It would help to know what your program is.

However from working the numbers it can easily be seen that:

P(N=n) (where n=#successes) = (nC4)(.5)^4
P(N=n)=0.0625(nC4)

from binomial theorem nC4 ~ {1,4,6,4,1}
i.e. 0C4 = 1 and 1C4 = 4...

So the cumulative function at any given point is the sum of the nC4 numbers times 0.0625...

P(N=0) = 1*0.0625
P(N=1)=(1+4)0.0625
P(N=2)=(1+4+6)0.0625 = 0.6875
P(N=3)=(1+4+6+4)0.0625 = 0.9375
P(N=4)=(1+4+6+4+1)0.0625 = 1

So your answer is 3.

Answer 2

P(n(51)>=11) = risk that the style of previous geezers is larger than or equivalent to 11 people. p(croak) = risk that a 50 yo guy will croak in a 12 months. p(no longer croak) = one million - p(croak). for this reason the risk that a minimum of 11 of those wheezers survives their 51st bday is the joint risk that 11 do no longer croak. that's, a minimum of 11 ought to proceed to exist given a risk of surviving for absolutely everyone at p(no longer croak) = one million - p(croak); the place p(croak) = .01125 In math communicate P(n(51)>=11) = p(no longer croak) X p(no longer croak) X ... X p(no longer croak) for 11 adult males, each having p(no longer croak) risk of surviving the 12 months. for this reason, P(n(51)>= 11) = p(no longer croak)^11 = (one million - .01125)^11; and you're able to do the mathematics. Lesson found out: Joint risk of self reliant activities (like a guy death or surviving) is basically the different of each journey. in this difficulty, we mandatory to comprehend the joint risk of a minimum of 11 geezers surviving to their 51st b'day. So we found the risk of no longer croaking (i.e., of surviving) for absolutely everyone and bigger that 11 situations to point the joint risk that a minimum of 11 proceed to exist. you could try the coolest judgment of a joint risk on your individual techniques by skill of asking this question "Will the risk of a minimum of a few extensive style surviving bypass up or down if we develop the extensive style who ought to proceed to exist?" in case you hit upon your joint risk is going up with bigger numbers, you have probable carried out something incorrect on your modeling. that's, it ought to be greater durable to get greater survivors, case in point, than fewer and greater durable interprets to diminish risk.