An electronics store has received a shipment of 20 table radios that have connec

Question

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 a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots.

(a) What kind of distribution does X have (name and values of all parameters)?

hypergeometric with N = 12, M = 6, and n = 12binomial with n = 12, x = 6, and p = 6/12    binomial with n = 20, x = 12, and p = 6/20hypergeometric with N = 20, M = 12, and n = 6

(b) Compute

P(X = 2), P(X 2), and P(X 2).

(Round your answers to four decimal places.)

(c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.)

Explanation / Answer

A) N = 20

6 TO BE CHOOSEN

12 ARE OF TWO SLOTS SO THE DISTRIBUTION WILL BE OF BINOMIAL N = 20, X = 12

OPTION C IS CORRECT.

B) PROBABILITY OF TWO SLOTS TYPE = 12/20 = 0.6

PROBABILITY OF NIN TWO SLOTS = 0.4

P(X=2) = 6C2*(0.6)^2*(0.4)^4 = 0.138

P(X<=2) = P(0)+P(1)+P(2) = 6C0*(0.6)^0*(0.4)^6 + 6C1*(0.6)^1*(0.4)^5 +P(2) = 0.004+0.03+0.138 = 0.172

P(X>=2) = 1 - P(0)+P(1) = 1- 0.004-0.03 = 0.966

C)E(X) = 0*P(0)+1*P(1)+2*P(2) = 0.294 = MEAN

VAR(X)= E(X^2) - E(X)^2 = 0.550 - 0.08 = 0.470

STANDARD DEV = 0.470^(1/2) = 0.68

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