Fill in the blank. 1.The set of all possible out comes in an experiment is descr

Question

Fill in the blank.
1.The set of all possible out comes in an experiment is describe by the ______ .
2.The _______ of two events A and B is the event in which both A and B occur.
3.Two events are said to be _____ if they can not occur at the same time.
4.The _____ of two events A and B is the event in which either A or B or both occur.
5.Two events are said to be _____ if the occurrence of one does not influence the probability of occurrence for the other.

6. If n = 5 how many different combinations of 3 are possible? 5 choose 3 = _____ .

7. A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.)

(a) What is the probability that at most 7 of the calls involve a fax message?

(b) What is the probability that exactly 7 of the calls involve a fax message?

(c) What is the probability that at least 7 of the calls involve a fax message?

(d) What is the probability that more than 7 of the calls involve a fax message?

Explanation / Answer

Q7.

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X = 7 ) = ( 20 7 ) * ( 0.2^7) * ( 1 - 0.2 )^13
= 0.0545
b.
P( X < = 7) = P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 20 7 ) * 0.2^7 * ( 1- 0.2 ) ^13 + ( 20 6 ) * 0.2^6 * ( 1- 0.2 ) ^14 + ( 20 5 ) * 0.2^5 * ( 1- 0.2 ) ^15 + ( 20 4 ) * 0.2^4 * ( 1- 0.2 ) ^16 + ( 20 3 ) * 0.2^3 * ( 1- 0.2 ) ^17 + ( 20 2 ) * 0.2^2 * ( 1- 0.2 ) ^18 + ( 20 1 ) * 0.2^1 * ( 1- 0.2 ) ^19 + ( 20 0 ) * 0.2^0 * ( 1- 0.2 ) ^20
= 0.9679
c.
P( X < 7) = P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 20 6 ) * 0.2^6 * ( 1- 0.2 ) ^14 + ( 20 5 ) * 0.2^5 * ( 1- 0.2 ) ^15 + ( 20 4 ) * 0.2^4 * ( 1- 0.2 ) ^16 + ( 20 3 ) * 0.2^3 * ( 1- 0.2 ) ^17 + ( 20 2 ) * 0.2^2 * ( 1- 0.2 ) ^18 + ( 20 1 ) * 0.2^1 * ( 1- 0.2 ) ^19 + ( 20 0 ) * 0.2^0 * ( 1- 0.2 ) ^20
= 0.9133
P( X > = 7 ) = 1 - P( X < 7) = 0.0867
d.
P( X > 7) = 1 - P ( X <=7) = 1 -0.9679 = 0.0321

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