(1 point) A certain type of digital camera comes in either a 3-megapixel version

Question

(1 point) A certain type of digital camera comes in either a 3-megapixel version or a 4-megapixel version. A camera store has received a shipment of 14 of these cameras, of which 6 have 3-megapixel resolution. Suppose that 5 of these cameras are randomly selected to be stored behind the counter; the other 9 are placed in a storeroom. Let X- the number of 3-megapixel cameras among the 5 selected for behind the counter storage. (b) Compute P(X > 2) (c) Calculate the mean of X. (d) Calculate the standard deviation of X.

Explanation / Answer

N = 14

k = 6

n = 5

a) P(X = 2) = 6C2 * 8C3 / 14C5 = 0.4196

b) P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5)

                  = 6C3 * 8C2 / 14C5 + 6C4 * 8C1 / 14C5 + 6C5 * 8C0 / 14C5

                  = 0.3427

c) Mean = n * k / N = 5 * 6 / 14 = 2.14

d) Variance = n * k * ( N - k ) * ( N - n ) / [ N2 * ( N - 1 ) ] = 5 * 6 * ( 14 - 6 ) * ( 14 - 5 ) / [ 142 * ( 14 - 1 ) ] = 0.8477

Standard deviation = sqrt(0.8477) = 0.9207

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