7. An electronics store has received a shipment of 20 table radios that have con

Question

7. An electronics store has received a shipment of 20 table radios that have connections for an iPod or iPhone. Twelve of these have two slots (so they can accommodate both devices), and the other eight have a single slot. Suppose that six of the 20 radios are randomly selected to be stored under shelf where the radios are displayed, and the remaining ones are placed in a storeroom, Let.'be the mumber amoug the radios stored under the display shelf that have two slots. a. What kind of a distribution does Xhave (name and values of all parameters)? b. Compute P(X = 2), P(X 2), P(X 2). c. Calculate the mean value and standard deviation of X

Explanation / Answer

Q1.
BIONOMIAL 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

Q2.
P( X = 2 ) = ( 6 2 ) * ( 0.6^2) * ( 1 - 0.6 )^4
= 0.13824

P( X < = 2) = P(X=2) + P(X=1) + P(X=0)   
= ( 6 2 ) * 0.6^2 * ( 1- 0.6 ) ^4 + ( 6 1 ) * 0.6^1 * ( 1- 0.6 ) ^5 + ( 6 0 ) * 0.6^0 * ( 1- 0.6 ) ^6
= 0.1792

P( X < 2) = P(X=1) + P(X=0)   
= ( 6 1 ) * 0.6^1 * ( 1- 0.6 ) ^5 + ( 6 0 ) * 0.6^0 * ( 1- 0.6 ) ^6
= 0.04096
P( X > = 2 ) = 1 - P( X < 2) = 0.95904

Q3.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 6 * 0.6
= 3.6
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 6 * 0.6 * 0.4
= 1.44
III.
standard deviation = sqrt( variance ) = sqrt(1.44)
=1.2

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