Question

Use Binomial Tables to answer #10 and #11, 12 below:

10. Assuming the coin is a fair coin, you flip a coin 11 times, what is the probability that
you would get exactly 7 heads?

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11. According to insurance records, a car with a certain protection system will be
recovered 90% of the time. Find the probability that, out of 7 cars, 5 or more would be recovered.
(Show work.)

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12. The probability that a football game will go into overtime is 16%.
Using the formal Binomial Formula, find the probability that, out of 14 football games, exactly 4
would go into overtime.

Answer 1

10) Let x be number of heads when a coin is flipped 11 times. Here x follows binomial distribution with parameters n=11 and p =0.5. The pdf of binomial distribution is, P(X= =) = (*) *(1-2)** :x=0,12 Compute the required probability. P(X=7={,0.5) (1-0,3)* 10) --. = 0.1611

11) Let x follows binomial distribution with parameters n = 7 and p = 0.90. The pdf of binomial distribution is, P(X =x) = (*) p*(1-p)** ;x=0,1,2,.. Compute the required probability. P(X 25) = P(X = 5) + P(X = 6) + P(X = 7) -6)(0.00'(-0.90)* +67)60,90,91–090)* +(7)(0.90)'(1-0,90)-2 0-..) = 0.1240+0.3720+0.4783 = 0.9743

12) Let x follows binomial distribution with parameters n=14 and p = 0.16 The pdf of binomial distribution is, P(X =x) = (*) p*(1-p)** ;x=0,1,2,... Compute the required probability. P(X=4) =(4)(0.16)*(10.16)** 03--1-2 = 0.1147