Amagle shop sells a coin which is rather bis ed. It comes up heads 71% of the ti

Question

Amagle shop sells a coin which is rather bis ed. It comes up heads 71% of the time. Suppose the shop owner puts on a demonstration his customers by Bipping the coin 12 times. For each item below, write the letter which corresponds to the correct value. Some letters may not be used and some letters may be used more than once. 2. Probability of exactly 6 heads? * Probability of more than 9 heads? Probability of at least 10 heads? Probability of less than 8 heads? .Mean/Expected value for the number of heads? Standard deviation for the number of heads? A. 0.070 B. 0.097 C. 0.103 D. 0.250 E. 0.278 F. 0.476 G. 0.500 H. 0.524 I. 1.572 J. 2.471 K. 3.480 L. 6.000 M. 8.520 PART II. MULTIPLE CHOICE-Circle the letter of the correct response 3. Let Z be a standard normal random variable. Find P(El> 6). Drawing a pieture may helpful. (a) 0.274 (b) 0.451 (c) 0.549 (d) 0.617 (e) 0.726

Explanation / Answer

Q2.

a.
P( X = 6 ) = ( 12 6 ) * ( 0.71^6) * ( 1 - 0.71 )^6
= 0.070406
b.
P( X < = 9) = P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) +
= ( 12 9 ) * 0.71^9 * ( 1- 0.71 ) ^3 + ( 12 8 ) * 0.71^8 * ( 1- 0.71 ) ^4 + ( 12 7 ) * 0.71^7 * ( 1- 0.71 ) ^5 + ( 12 6 ) * 0.71^6 * ( 1- 0.71 ) ^6 + ( 12 5 ) * 0.71^5 * ( 1- 0.71 ) ^7 + ( 12 4 ) * 0.71^4 * ( 1- 0.71 ) ^8 + ( 12 3 ) * 0.71^3 * ( 1- 0.71 ) ^9 + ( 12 2 ) * 0.71^2 * ( 1- 0.71 ) ^10 + ( 12 1 ) * 0.71^1 * ( 1- 0.71 ) ^11 + ( 12 0 ) * 0.71^0 * ( 1- 0.71 ) ^12 +  
= 0.722
P( X > 9) = 1 - P ( X <=9) = 1 -0.722 = 0.278
c.
P( X < 10) = P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) +  
= ( 12 9 ) * 0.71^9 * ( 1- 0.71 ) ^3 + ( 12 8 ) * 0.71^8 * ( 1- 0.71 ) ^4 + ( 12 7 ) * 0.71^7 * ( 1- 0.71 ) ^5 + ( 12 6 ) * 0.71^6 * ( 1- 0.71 ) ^6 + ( 12 5 ) * 0.71^5 * ( 1- 0.71 ) ^7 + ( 12 4 ) * 0.71^4 * ( 1- 0.71 ) ^8 + ( 12 3 ) * 0.71^3 * ( 1- 0.71 ) ^9 + ( 12 2 ) * 0.71^2 * ( 1- 0.71 ) ^10 + ( 12 1 ) * 0.71^1 * ( 1- 0.71 ) ^11 + ( 12 0 ) * 0.71^0 * ( 1- 0.71 ) ^12 +
= 0.722
P( X > = 10 ) = 1 - P( X < 10) = 0.278
d.
P( X < 8) = P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) +   
= ( 12 7 ) * 0.71^7 * ( 1- 0.71 ) ^5 + ( 12 6 ) * 0.71^6 * ( 1- 0.71 ) ^6 + ( 12 5 ) * 0.71^5 * ( 1- 0.71 ) ^7 + ( 12 4 ) * 0.71^4 * ( 1- 0.71 ) ^8 + ( 12 3 ) * 0.71^3 * ( 1- 0.71 ) ^9 + ( 12 2 ) * 0.71^2 * ( 1- 0.71 ) ^10 + ( 12 1 ) * 0.71^1 * ( 1- 0.71 ) ^11 + ( 12 0 ) * 0.71^0 * ( 1- 0.71 ) ^12 +
= 0.25
e.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 12 * 0.71
= 8.52
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 12 * 0.71 * 0.29
= 2.471
III.
standard deviation = sqrt( variance ) = sqrt(2.471)
=1.572

i-> A
ii-> E
iii-> E
iV -> D
v -> M
vi -> I

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