Suppose an organization makes phone calls to solicit donations 30% of the number

Question

Suppose an organization makes phone calls to solicit donations 30% of the numbers in its database are landlines, and the other 70% are cellphones. From past experience the organization knows that of landlines called, 52% do not donate, 33% donate between $1 and $19 distributed uniformly, and the remaining 15% donate between $1 and $19 distributed uniformly. The organization also knows that of cellphones called, 61% do not donate, 29% donate between $1 and $19 distributed uniformly, and the remaining 10% donate between $20 and $50 distributed uniformly. What is the probability that the next call the organization makes at least $20? If the next person the organization calls doesn't donate, what is the probability that it was a landline number? Suppose the next person donates between $20 and $50. What is that person's expected donation? Let random variable X represent the amount of money the organization makes from the next call. What is E(X)?

Explanation / Answer

A) P(at least 20) = P(at least $20 from landline) + P(at least $20 from cellphone)

= 0.3x0.15 + 0.7x0.1 = 0.115

B) P (landline | doesn't donate) = P(landline and doesnt donate)/P(doesnt donate)

= 0.3x0.52/(0.3x0.52 + 0.7x 0.61)

= 0.2676

C) Expected donation = (20+50)/2 = $35

D) E(X) = 0.3(0 + 10x0.33 + 35x0.15) + 0.7(0 + 10x0.29 + 35x0.1)

= 2.565 + 4.48

= $7.045

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