please answer all parts thanks a lot 3a) A certain type of digital camera comes

Question

please answer all parts
thanks a lot

3a) A certain type of digital camera comes either a 3-megapixel version or a 4-megapixel 5 version. A camera store has received a shipment of 15 of these cameras, of which 6 have 3-magepixel. Suppose that 5 of these cameras are randomly selected without replacement. (i) What is the distribution of the number of 3-megapixel cameras among the 5 selected? (a) Binomial (b) Hypergeometric (c) Poisson (choose one). (ii) What is the probability that at most one 3-megapixel camera among the 5 selected?

Explanation / Answer

i) Binomial Distribution , because no. of cameras are finite and there are only two outcomes (i.e. either 3Megapixel or 4Megapixel) and probability of selecting 3 Megapixel is constant.

Parameters are n = 5, p =6/15 =0.4

ii)

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

=(5C0) (0.4)0 (0.6)5 + (5C1)(0.4)(0.6)4 = 0.0778+0.2592 = 0.337

iii) Mean =np = 5*0.4 = 2

variance = npq = 5*0.4*0.6 = 1.2

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