declial tosses six coins. Fill in the following Binomial Table: Use four P(x) P(

Question

declial tosses six coins. Fill in the following Binomial Table: Use four P(x) P(x or fewer) P(x or greater) x = # Heads 4 6 A) Find the probability that exactly 5 coins landed heads. B) Find the probability that exactly 4 coins landed tails. C) Find the probability that less than 3 coins landed heads. D) Find the probability that 2 or more coins landed heads. Find the probability that at least one landed heads. E) F) Find the probability that no more than 2 landed heads. G) What is the mean of the binomial distribution? H) What is the standard deviation of the binomial distribution? l) What random variables would be considered unusual?

Explanation / Answer

Tosses six coines

Here Pr(Head) = Pr(Tail) = 0.5

(A) Pr(X = 5) = 6C5 (0.5)6 = 0.09375

(B) Pr(X = 2 as number of tails are 4) =   6C2 (0.5)2 = 0.234375

(C) Pr(X < 3 heads) = 0.34375

(D) Pr(X   2 heads) = 0.890625

(E) Pr(X 1 head) = 0.984375

(F) Pr(X 2 heads) = 0.34375

(G) Mean of binomial distribution = 6 * 0.5 = 3

(H) Standard deviation = sqrt (6 * 0.5 * 0.5)= 1.225

(I) Here as X = 1 and and X = 6 that means obtaining one head or 6 head can be considered unusual as the probability of that happening is less than 0.05.

x = # heads P(x) P(x or fewer) P(x or greater) 0 0.015625 0.015625 1 1 0.09375 0.109375 0.984375 2 0.234375 0.34375 0.890625 3 0.3125 0.65625 0.65625 4 0.234375 0.890625 0.34375 5 0.09375 0.984375 0.109375 6 0.015625 1 0.015625

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