A company is in the business of finding addresses of long-lost friends. The comp

Question

A company is in the business of finding addresses of long-lost friends. The company claims to have a 70% success rate. Suppose that you have the names of eight friends for whom you have no addresses and decide to use the company to track them.

(a) Make a histogram showing the probability of r = 0 to 8 friends for whom an address will be found.

(b) Find the mean and standard deviation of this probability distribution. What is the expected number of friends for whom addresses will be found? (Round your answers to two decimal places.)

(c) How many names would you have to submit to be 97% sure that at least two addresses will be found? (Enter your answer as a whole number.)
names

0.25 0.2 0.15 P(r) 0.1 0.05 1 3 4 5 6 7 8

Explanation / Answer

(a)

If we calculate the probabilities, below is the table

The graph shows these values is graph 2.

(b)

mean = 0.7 * 8 = 5.6
sigma = sqrt(0.7*0.3*8) = 1.2961

(c)
For 97%, z-value = 1.88
Hence required number = 5.6 + 1.88*1.2961 = 8 (approximately)

r P(X=r) 0 0.00007 1 0.00122 2 0.01000 3 0.04668 4 0.13614 5 0.25412 6 0.29648 7 0.19765 8 0.05765

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