A marketing agency has developed three vacation packages to promote a timeshare

Question

A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 10% of potential customers will choose the Day Plan, which does not include overnight accommodations; 20% will choose the Overnight Plan, which includes one night at the resort; and 70% will choose the Weekend Plan, which includes two nights. Complete parts a and b below.

a) Find the expected value of the number of nights potential customers will need.

E(X)= _____ of nights

b) Find the standard deviation of the number of nights potential customers will need.

= _________ of nights

Explanation / Answer

(a) E(x) = Sum [x*P(x)] = 0 * 0.1 + 1 * 0.2 + 2 * 0.7 = 0 + 0.2 + 1.4 = 1.6 of nights

(b) Standard deviation = Sqrt(Variance)

Variance = E[X2] = [E(x)]2.

[E(x)]2= 1.6 * 1.6 = 2.56 and

E[X2] = Sum [x2.P(x)] = 02 * 0.1 + 12 * 0.2 + 22 * 0.7 = 0 + 0.2 + 2.8 = 3

Therefore Variance = 3 - 2.56 = 0.44 and

Standard deviation = Sqrt(0.44) = 0.6633 of nights

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