An electronics store has received a shipment of 25 table radios that have connec

Question

An electronics store has received a shipment of 25 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 thirteen have a single slot. Suppose that eight of the 25 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.

1. Compute

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

(Round your answers to four decimal places.)

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

Explanation / Answer

This is hypergeometric distribution with N = 25, k = 12, n = 8

1) P(X = 2) = 12C2 * 13C6) / 25C8 = 66 * 1716 / 1081575 = 0.1047

P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

               = 12C0 * 13C8 / 25C8 + 12C1 * 13C7 / 25C8 + 12C2 * 13C6 / 25C8

               =0.1249

P(X > 2) = 1 - [P(X < 2) - P(X = 2)]

              = 1 - 0.1249 + 0.1047

              = 0.9798

2) Mean = n * k / N = 8 * 12 / 25 = 3.84

Variance = n * k * ( N - k ) * ( N - n ) / [ N2 * ( N - 1 ) ] .= 8 * 12 * ( 25 - 12 ) * ( 25 - 8 ) / [ 252 * ( 25 - 1 ) ] = 1.4144

Standard deviation = sqrt(1.4144) = 1.19

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